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Journal articles on the topic 'Global and local optimizations'

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Published: 25 May 2024

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1

Ravi Kiran, B., and Jean Serra. "Global–local optimizations by hierarchical cuts and climbing energies." Pattern Recognition 47, no. 1 (January 2014): 12–24. http://dx.doi.org/10.1016/j.patcog.2013.05.012.

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2

Wang, Wei, Xiaoshan Zhang, and Min Li. "A Filled Function Method Dominated by Filter for Nonlinearly Global Optimization." Journal of Applied Mathematics 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/245427.

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This work presents a filled function method based on the filter technique for global optimization. Filled function method is one of the effective methods for nonlinear global optimization, since it can effectively find a better minimizer. Filter technique is applied to local optimization methods for its excellent numerical results. In order to optimize the filled function method, the filter method is employed for global optimizations in this method. A new filled function is proposed first, and then the algorithm and its properties are proved. The numerical results are listed at the end.

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Li, Shuang, and Qiuwei Li. "Local and Global Convergence of General Burer-Monteiro Tensor Optimizations." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (June 28, 2022): 10266–74. http://dx.doi.org/10.1609/aaai.v36i9.21267.

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Tensor optimization is crucial to massive machine learning and signal processing tasks. In this paper, we consider tensor optimization with a convex and well-conditioned objective function and reformulate it into a nonconvex optimization using the Burer-Monteiro type parameterization. We analyze the local convergence of applying vanilla gradient descent to the factored formulation and establish a local regularity condition under mild assumptions. We also provide a linear convergence analysis of the gradient descent algorithm started in a neighborhood of the true tensor factors. Complementary to the local analysis, this work also characterizes the global geometry of the best rank-one tensor approximation problem and demonstrates that for orthogonally decomposable tensors the problem has no spurious local minima and all saddle points are strict except for the one at zero which is a third-order saddle point.

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4

Lazzaretto, Andrea, Andrea Toffolo, Matteo Morandin, and Michael R. von Spakovsky. "Criteria for the decomposition of energy systems in local/global optimizations." Energy 35, no. 2 (February 2010): 1157–63. http://dx.doi.org/10.1016/j.energy.2009.06.009.

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5

Yang, Dezhi, Xintong He, Jun Wang, Guoxian Yu, Carlotta Domeniconi, and Jinglin Zhang. "Federated Causality Learning with Explainable Adaptive Optimization." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 15 (March 24, 2024): 16308–15. http://dx.doi.org/10.1609/aaai.v38i15.29566.

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Discovering the causality from observational data is a crucial task in various scientific domains. With increasing awareness of privacy, data are not allowed to be exposed, and it is very hard to learn causal graphs from dispersed data, since these data may have different distributions. In this paper, we propose a federated causal discovery strategy (FedCausal) to learn the unified global causal graph from decentralized heterogeneous data. We design a global optimization formula to naturally aggregate the causal graphs from client data and constrain the acyclicity of the global graph without exposing local data. Unlike other federated causal learning algorithms, FedCausal unifies the local and global optimizations into a complete directed acyclic graph (DAG) learning process with a flexible optimization objective. We prove that this optimization objective has a high interpretability and can adaptively handle homogeneous and heterogeneous data. Experimental results on synthetic and real datasets show that FedCausal can effectively deal with non-independently and identically distributed (non-iid) data and has a superior performance.

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Zatolokin, Y. A., E. I. Vatutin, and V. S. Titov. "ALGORITHMIC OPTIMIZATION OF SOFTWARE IMPLEMENTATION OF ALGORITHMS FOR MULTIPLYING DENSE REAL MATRICES ON GRAPHICS PROCESSORS WITH OPENGL TECHNOLOGY SUPPORT." Proceedings of the Southwest State University 21, no. 5 (October 28, 2017): 6–15. http://dx.doi.org/10.21869/2223-1560-2017-21-5-06-15.

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In the article was given statement of a problem of matrix multiplication. Is is show that desired problem can be simpl formulated but for its solving may be required both heuristic methods and set of algorithmic modifications relating to algorithmic and high-level software optimization taking into account the particular problem and allow to increase the multiplication performance. These include: a comparative analysis of the performance of the actions performed without GPU-specific optimizations and with optimizations, which showed that computations without optimizing the work with global GPU memory have low processing performance. Optimizing data distribution in global and local memory The GPU allows you to reuse the calculation time and increase real performance. To compare the performance of the developed software implementations for OpenGL and CUDA technologies, identical calculations on identical GPUs were performed, which showed higher real performance when using CUDA cores. Specific values of generation performance measured for multi-threaded software implementation on GPU are given for all of described optimizations. It is shown that the most effective approach is based on the method we can get much more performance by technique of caching sub-blocks of the matrices (tiles) in the GPU's on-chip local memory, that with specialized software implementation is provide the performance of 275,3 GFLOP/s for GPU GeForce GTX 960M.

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Bao, Rong, Yongdong Li, Hongguang Wang, and Chunliang Liu. "A Multi-Constrained Optimization Method for THz Backward Wave Oscillators." Applied Sciences 12, no. 20 (October 20, 2022): 10583. http://dx.doi.org/10.3390/app122010583.

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The current design period for various backward wave oscillators (BWOs) is still at least several months. How to find the best structure parameters with an efficient and stable optimization method is a problem facing researchers in both scientific research and engineering work. In this paper, a non-randomized iterative optimization method is proposed. It applies orthogonal design methods to find local solutions that can provide optimal ‘gradient direction’ for several successive next iteration steps. An evaluation function is designed to distinguish the better ones from the local solutions in the multi-constrained optimization of such BWOs. Optimizations from different starting points are performed separately for a global optimal solution. Two BWOs at different frequency ranges are optimized using the proposed method. The validity and stability of the method are verified. It is believed that the method can provide the global optimum and shorten the design period of THz BWOs.

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8

Tohka, Jussi. "GLOBAL DEFORMABLE SURFACE OPTIMIZATION USING ADAPTIVE CONSTRAINTS AND PENALTIES." Image Analysis & Stereology 24, no. 1 (May 3, 2011): 9. http://dx.doi.org/10.5566/ias.v24.p9-19.

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Deformable models are able to solve surface extraction problems challenged by image noise because imageindependent constraints are used to regularize the shape of the extracted surface. However, this ability of deformable models is shadowed by their application specificity, initialization sensitivity and the difficulty of the selection of proper values for user definable parameters. To overcome these problems restricting the automation of surface extraction, we present a new algorithm, named AdaCoP, for the global minimization of the energy of deformable surfaces. It iteratively performs constrained local minimizations of the energy. It avoids the detection of the same local minimum multiple times by constraining the local optimizations in an adaptive manner. AdaCoP escapes from local minima by imposing an adaptive penalty energy to it. These constraints and penalties prevent the convergence to the local minima already found. The performance of the AdaCoP algorithm is relatively independent on the nature of the underlying image as well as the shape of the surface to be extracted. The performance of the algorithm is evaluated by extracting surfaces from synthetic images. Moreover, the good properties of the algorithm are demonstrated by considering applications within the automated analysis of positron emission tomography images. Although AdaCoP cannot be proven to converge to the global minimum, it is insensitive to its initialization and it therefore provides a way to automate surface extraction problems within medical image analysis.

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9

Jia, Jia, and Dejun Mu. "Low-Energy-Orientated Resource Scheduling in Cloud Computing by Particle Swarm Optimization." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 2 (April 2018): 339–44. http://dx.doi.org/10.1051/jnwpu/20183620339.

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In order to reduce the energy cost in cloud computing, this paper represents a novel energy-orientated resource scheduling method based on particle swarm optimization. The energy cost model in cloud computing environment is studied first. The optimization of energy cost is then considered as a multiobjective optimization problem, which generates the Pareto optimization set. To solve this multiobjective optimization problem, the particle swarm optimization is involved. The states of one particle consist of both the allocation plan for servers and the frequency plans on servers. Each particle in this algorithm obtains its Pareto local optimization. After the assembly of local optimizations, the algorithm generates the Pareto global optimization for one server plan. The final solution to our problem is the optimal one among all server plans. Experimental results show the good performance of the proposed method. Comparing with the widely-used Round robin scheduling method, the proposed method requires only 45.5% dynamic energy cost.

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10

Grunbacher, Sophie, Ramin Hasani, Mathias Lechner, Jacek Cyranka, Scott A. Smolka, and Radu Grosu. "On the Verification of Neural ODEs with Stochastic Guarantees." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 13 (May 18, 2021): 11525–35. http://dx.doi.org/10.1609/aaai.v35i13.17372.

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We show that Neural ODEs, an emerging class of time-continuous neural networks, can be verified by solving a set of global-optimization problems. For this purpose, we introduce Stochastic Lagrangian Reachability (SLR), an abstraction-based technique for constructing a tight Reachtube (an over-approximation of the set of reachable states over a given time-horizon), and provide stochastic guarantees in the form of confidence intervals for the Reachtube bounds. SLR inherently avoids the infamous wrapping effect (accumulation of over-approximation errors) by performing local optimization steps to expand safe regions instead of repeatedly forward-propagating them as is done by deterministic reachability methods. To enable fast local optimizations, we introduce a novel forward-mode adjoint sensitivity method to compute gradients without the need for backpropagation. Finally, we establish asymptotic and non-asymptotic convergence rates for SLR.

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11

Jianqi, Shi, Huang Yanhong, Li Ang, and Cai Fangda. "An optimal solution for software testing case generation based on particle swarm optimization." Open Physics 16, no. 1 (June 21, 2018): 355–63. http://dx.doi.org/10.1515/phys-2018-0048.

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AbstractSearching based testing case generation technology converts the problem of testing case generation to function optimizations, through a fitness function, which is usually optimized using heuristic search algorithms. The particle swarm optimization (PSO) optimized testing case generation algorithm tends to lose population diversity of locally optimal solutions with low accuracy of local search. To overcome the above defects, a self-adaptive PSO based software testing case optimization algorithm is proposed. It adjusts the inertia weight dynamically according to the current iteration and average relative speed, to improve the performance of standard PSO. An improved alternating variable method is put forward to accelerate local search speed, which can coordinate both global and local search ability thereby improving the overall generation efficiency of testing cases. The experimental results demonstrate that the approach outlined here keeps higher testing case generation efficiency, and it shows certain advantages in coverage, evolution generation amount and running time when compared to standard PSO and GA-PSO.

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12

Meng, Yufeng, Jianhua He, Shichu Luo, Siqi Tao, and Jiancheng Xu. "An improved predator-prey particle swarm optimization algorithm for Nash equilibrium solution." PLOS ONE 16, no. 11 (November 24, 2021): e0260231. http://dx.doi.org/10.1371/journal.pone.0260231.

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Focusing on the problem incurred during particle swarm optimization (PSO) that tends to fall into local optimization when solving Nash equilibrium solutions of games, as well as the problem of slow convergence when solving higher order game pay off matrices, this paper proposes an improved Predator-Prey particle swarm optimization (IPP-PSO) algorithm based on a Predator-Prey particle swarm optimization (PP-PSO) algorithm. First, the convergence of the algorithm is advanced by improving the distribution of the initial predator and prey. By improving the inertia weight of both predator and prey, the problem of “precocity” of the algorithm is improved. By improving the formula used to represent particle velocity, the problems of local optimizations and slowed convergence rates are solved. By increasing pathfinder weight, the diversity of the population is increased, and the global search ability of the algorithm is improved. Then, by solving the Nash equilibrium solution of both a zero-sum game and a non-zero-sum game, the convergence speed and global optimal performance of the original PSO, the PP-PSO and the IPP-PSO are compared. Simulation results demonstrated that the improved Predator-Prey algorithm is convergent and effective. The convergence speed of the IPP-PSO is significantly higher than that of the other two algorithms. In the simulation, the PSO does not converge to the global optimal solution, and PP-PSO approximately converges to the global optimal solution after about 40 iterations, while IPP-PSO approximately converges to the global optimal solution after about 20 iterations. Furthermore, the IPP-PSO is superior to the other two algorithms in terms of global optimization and accuracy.

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13

Li, Li, Liu, and Ruan. "An Improved Bat Algorithm Based on Lévy Flights and Adjustment Factors." Symmetry 11, no. 7 (July 15, 2019): 925. http://dx.doi.org/10.3390/sym11070925.

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This paper proposed an improved bat algorithm based on Lévy flights and adjustment factors (LAFBA). Dynamically decreasing inertia weight is added to the velocity update, which effectively balances the global and local search of the algorithm; the search strategy of Lévy flight is added to the position update, so that the algorithm maintains a good population diversity and the global search ability is improved; and the speed adjustment factor is added, which effectively improves the speed and accuracy of the algorithm. The proposed algorithm was then tested using 10 benchmark functions and 2 classical engineering design optimizations. The simulation results show that the LAFBA has stronger optimization performance and higher optimization efficiency than basic bat algorithm and other bio-inspired algorithms. Furthermore, the results of the real-world engineering problems demonstrate the superiority of LAFBA in solving challenging problems with constrained and unknown search spaces.

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14

HONG, Liang, Sensen CHU, Shuangyun PENG, and Quanli XU. "Multiscale segmentation-optimized algorithm for high-spatial remote sensing imagery considering global and local optimizations." National Remote Sensing Bulletin 24, no. 12 (2020): 1464–75. http://dx.doi.org/10.11834/jrs.20208496.

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15

Beheshti, Zahra, Siti Mariyam Shamsuddin, and Sarina Sulaiman. "Fusion Global-Local-Topology Particle Swarm Optimization for Global Optimization Problems." Mathematical Problems in Engineering 2014 (2014): 1–19. http://dx.doi.org/10.1155/2014/907386.

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In recent years, particle swarm optimization (PSO) has been extensively applied in various optimization problems because of its structural and implementation simplicity. However, the PSO can sometimes find local optima or exhibit slow convergence speed when solving complex multimodal problems. To address these issues, an improved PSO scheme called fusion global-local-topology particle swarm optimization (FGLT-PSO) is proposed in this study. The algorithm employs both global and local topologies in PSO to jump out of the local optima. FGLT-PSO is evaluated using twenty (20) unimodal and multimodal nonlinear benchmark functions and its performance is compared with several well-known PSO algorithms. The experimental results showed that the proposed method improves the performance of PSO algorithm in terms of solution accuracy and convergence speed.

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16

Addis, Bernardetta, Marco Locatelli, and Fabio Schoen. "Local optima smoothing for global optimization." Optimization Methods and Software 20, no. 4-5 (August 2005): 417–37. http://dx.doi.org/10.1080/10556780500140029.

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17

Locatelli, Marco, and Fabio Schoen. "Global optimization based on local searches." Annals of Operations Research 240, no. 1 (September 22, 2015): 251–70. http://dx.doi.org/10.1007/s10479-015-2014-2.

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18

Locatelli, Marco, and Fabio Schoen. "Global optimization based on local searches." 4OR 11, no. 4 (November 16, 2013): 301–21. http://dx.doi.org/10.1007/s10288-013-0251-2.

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19

Rebello, Carine M., Márcio A. F. Martins, José M. Loureiro, Alírio E. Rodrigues, Ana M. Ribeiro, and Idelfonso B. R. Nogueira. "From an Optimal Point to an Optimal Region: A Novel Methodology for Optimization of Multimodal Constrained Problems and a Novel Constrained Sliding Particle Swarm Optimization Strategy." Mathematics 9, no. 15 (July 30, 2021): 1808. http://dx.doi.org/10.3390/math9151808.

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The present work proposes a novel methodology for an optimization procedure extending the optimal point to an optimal area based on an uncertainty map of deterministic optimization. To do so, this work proposes the deductions of a likelihood-based test to draw confidence regions of population-based optimizations. A novel Constrained Sliding Particle Swarm Optimization algorithm is also proposed that can cope with the optimization procedures characterized by multi-local minima. There are two open issues in the optimization literature, uncertainty analysis of the deterministic optimization and application of meta-heuristic algorithms to solve multi-local minima problems. The proposed methodology was evaluated in a series of five benchmark tests. The results demonstrated that the methodology is able to identify all the local minima and the global one, if any. Moreover, it was able to draw the confidence regions of all minima found by the optimization algorithm, hence, extending the optimal point to an optimal region. Moreover, providing the set of decision variables that can give an optimal value, with statistical confidence. Finally, the methodology is evaluated to address a case study from chemical engineering; the optimization of a complex multifunctional process where separation and reaction are processed simultaneously, a true moving bed reactor. The method was able to efficiently identify the two possible optimal operating regions of this process. Therefore, proving the practical application of this methodology.

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20

Bračevac, Oliver, Guannan Wei, Songlin Jia, Supun Abeysinghe, Yuxuan Jiang, Yuyan Bao, and Tiark Rompf. "Graph IRs for Impure Higher-Order Languages: Making Aggressive Optimizations Affordable with Precise Effect Dependencies." Proceedings of the ACM on Programming Languages 7, OOPSLA2 (October 16, 2023): 400–430. http://dx.doi.org/10.1145/3622813.

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Graph-based intermediate representations (IRs) are widely used for powerful compiler optimizations, either interprocedurally in pure functional languages, or intraprocedurally in imperative languages. Yet so far, no suitable graph IR exists for aggressive global optimizations in languages with both effects and higher-order functions: aliasing and indirect control transfers make it difficult to maintain sufficiently granular dependency information for optimizations to be effective. To close this long-standing gap, we propose a novel typed graph IR combining a notion of reachability types with an expressive effect system to compute precise and granular effect dependencies at an affordable cost while supporting local reasoning and separate compilation. Our high-level graph IR imposes lexical structure to represent structured control flow and nesting, enabling aggressive and yet inexpensive code motion and other optimizations for impure higher-order programs. We formalize the new graph IR based on a λ-calculus with a reachability type-and-effect system along with a specification of various optimizations. We present performance case studies for tensor loop fusion, CUDA kernel fusion, symbolic execution of LLVM IR, and SQL query compilation in the Scala LMS compiler framework using the new graph IR. We observe significant speedups of up to 21 x .

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21

Roy, Jarrod A., David A. Papa, and Igor L. Markov. "Fine Control of Local Whitespace in Placement." VLSI Design 2008 (September 23, 2008): 1–10. http://dx.doi.org/10.1155/2008/517919.

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In modern design methodologies, a large fraction of chip area during placement is left unused by standard cells and allocated as “whitespace.” This is done for a variety of reasons including the need for subsequent buffer insertion, as a means to ensure routability, signal integrity, and low coupling capacitance between wires, and to improve yield through DFM optimizations. To this end, layout constraints often require a certain minimum fraction of whitespace in each region of the chip. Our work introduces several techniques for allocation of whitespace in global, detail, and incremental placement. Our experiments show how to efficiently improve wirelength by reallocating whitespace in legal placements at the large scale. Additionally, for the first time in the literature, we empirically demonstrate high-precision control of whitespace in designs with macros and obstacles. Our techniques consistently improve the quality of whitespace allocation of top-down as well as analytical placement methods and achieve low penalties on designs from the ISPD 2006 placement contest with minimal interconnect increase.

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22

LI, Wei, Wen-biao JIN, and Xian-qian XIAO. "Local-global algorithm for triangular mesh optimization." Journal of Computer Applications 31, no. 4 (June 8, 2011): 1013–15. http://dx.doi.org/10.3724/sp.j.1087.2011.01013.

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23

Onodera, Tatsuhiro, Kenichi Tamura, and Keiichiro Yasuda. "Integrated Optimization Using Global and Local Modeling." Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2013 (May 5, 2013): 137–43. http://dx.doi.org/10.5687/sss.2013.137.

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24

Cheng, Xuemin, Yongtian Wang, Qun Hao, and Masaki Isshiki. "Global and local optimization for optical systems." Optik 117, no. 3 (March 2006): 111–17. http://dx.doi.org/10.1016/j.ijleo.2005.06.007.

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25

Deissenberg, Christophe. "The global failure of local preference optimization." Computers & Mathematics with Applications 25, no. 10-11 (May 1993): 161–72. http://dx.doi.org/10.1016/0898-1221(93)90290-c.

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26

Floudas, C. A., and H. Th Jongen. "Global Optimization: Local Minima and Transition Points." Journal of Global Optimization 32, no. 3 (July 2005): 409–15. http://dx.doi.org/10.1007/s10898-004-0865-1.

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Bagirov, Adil M., Alexander M. Rubinov, and Jiapu Zhang. "Local Optimization Method with Global Multidimensional Search." Journal of Global Optimization 32, no. 2 (June 2005): 161–79. http://dx.doi.org/10.1007/s10898-004-2700-0.

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28

Ahandani, Morteza Alinia, Mohammad-Taghi Vakil-Baghmisheh, and Mohammad Talebi. "Hybridizing local search algorithms for global optimization." Computational Optimization and Applications 59, no. 3 (March 15, 2014): 725–48. http://dx.doi.org/10.1007/s10589-014-9652-1.

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29

First, Z., S. T. Hackman, and U. Passy. "Local-global properties of bifunctions." Journal of Optimization Theory and Applications 73, no. 2 (May 1992): 279–97. http://dx.doi.org/10.1007/bf00940182.

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30

Kang, Chao, Jihui Xu, and Yuan Bian. "Affine Formation Maneuver Control for Multi-Agent Based on Optimal Flight System." Applied Sciences 14, no. 6 (March 8, 2024): 2292. http://dx.doi.org/10.3390/app14062292.

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The use of affine maneuver control to maintain the desired configuration of unmanned aerial vehicle (UAV) swarms has been widely practiced. Nevertheless, the lack of capability to interact with obstacles and navigate autonomously could potentially limit its extension. To address this problem, we present an innovative formation flight system featuring a virtual leader that seamlessly integrates global control and local control, effectively addressing the limitations of existing methods that rely on fixed configuration changes to accommodate real-world constraints. To enhance the elasticity of an algorithm for configuration change in an obstacle-laden environment, this paper introduces a second-order differentiable virtual force-based metric for planning local trajectories. The virtual field comprises several artificial potential field (APF) forces that adaptively adjust the formation compared to the existing following control. Then, a distributed and decoupled trajectory optimization framework that considers obstacle avoidance and dynamic feasibility is designed. This novel multi-agent agreement strategy can efficiently coordinate the global planning and local trajectory optimizations of the formation compared to a single method. Finally, an affine-based maneuver approach is employed to validate an optimal formation control law for ensuring closed-loop system stability. The simulation results demonstrate that the proposed scheme improves track accuracy by 32.92% compared to the traditional method, while also preserving formation and avoiding obstacles simultaneously.

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Bodyanskiy, Yevgeniy, Alina Shafronenko, and Iryna Pliss. "Credibilistic fuzzy clustering based on evolutionary method of crazy cats." System research and information technologies, no. 3 (November 18, 2021): 110–19. http://dx.doi.org/10.20535/srit.2308-8893.2021.3.09.

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The problem of fuzzy clustering of large datasets that are sent for processing in both batch and online modes, based on a credibilistic approach, is considered. To find the global extremum of the credibilistic fuzzy clustering goal function, the modification of the swarm algorithm of crazy cats swarms was introduced, that combined the advantages of evolutionary algorithms and a global random search. It is shown that different search modes are generated by a unified mathematical procedure, some cases of which are known algorithms for both local and global optimizations. The proposed approach is easy to implement and is characterized by the high speed and reliability in problems of multi-extreme fuzzy clustering.

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Garcia-Palomares, U. M., F. J. Gonzalez-Castaño, and J. C. Burguillo-Rial. "A Combined Global & Local Search (CGLS) Approach to Global Optimization." Journal of Global Optimization 34, no. 3 (March 2006): 409–26. http://dx.doi.org/10.1007/s10898-005-3249-2.

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Zhan, Dawei, Jiachang Qian, and Yuansheng Cheng. "Balancing global and local search in parallel efficient global optimization algorithms." Journal of Global Optimization 67, no. 4 (July 18, 2016): 873–92. http://dx.doi.org/10.1007/s10898-016-0449-x.

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KERDKAEW, JUTAMAS, RABIAN WANGKEEREE, and GUE MYUNG LEE. "On optimality conditions for robust weak sharp solution in uncertain optimizations." Carpathian Journal of Mathematics 36, no. 3 (September 30, 2020): 443–52. http://dx.doi.org/10.37193/cjm.2020.03.12.

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In this paper, we investigate the robust optimization problem involving nonsmooth and nonconvex real-valued functions. We firstly establish a necessary condition for the local robust weak sharp solution of considered problem under a constraint qualification. These optimality conditions are presented in terms of multipliers and Mordukhovich subdifferentials of the related functions. Then, by employing the robust version of the (KKT) condition, and some appropriate generalized convexity conditions, we also obtain some sufficient conditions for the global robust weak sharp solutions of the problem. In addition, some examples are presented for illustrating or supporting the results.

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35

Awotunde, Abeeb A. "GLOCAL: A global-local optimization template for multiple history-matched reservoir parameters." Journal of Petroleum Science and Engineering 154 (June 2017): 1–18. http://dx.doi.org/10.1016/j.petrol.2017.04.007.

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36

Jiang, Meirui, Zirui Wang, and Qi Dou. "HarmoFL: Harmonizing Local and Global Drifts in Federated Learning on Heterogeneous Medical Images." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 1 (June 28, 2022): 1087–95. http://dx.doi.org/10.1609/aaai.v36i1.19993.

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Multiple medical institutions collaboratively training a model using federated learning (FL) has become a promising solution for maximizing the potential of data-driven models, yet the non-independent and identically distributed (non-iid) data in medical images is still an outstanding challenge in real-world practice. The feature heterogeneity caused by diverse scanners or protocols introduces a drift in the learning process, in both local (client) and global (server) optimizations, which harms the convergence as well as model performance. Many previous works have attempted to address the non-iid issue by tackling the drift locally or globally, but how to jointly solve the two essentially coupled drifts is still unclear. In this work, we concentrate on handling both local and global drifts and introduce a new harmonizing framework called HarmoFL. First, we propose to mitigate the local update drift by normalizing amplitudes of images transformed into the frequency domain to mimic a unified imaging setting, in order to generate a harmonized feature space across local clients. Second, based on harmonized features, we design a client weight perturbation guiding each local model to reach a flat optimum, where a neighborhood area of the local optimal solution has a uniformly low loss. Without any extra communication cost, the perturbation assists the global model to optimize towards a converged optimal solution by aggregating several local flat optima. We have theoretically analyzed the proposed method and empirically conducted extensive experiments on three medical image classification and segmentation tasks, showing that HarmoFL outperforms a set of recent state-of-the-art methods with promising convergence behavior. Code is available at: https://github.com/med-air/HarmoFL

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Mao, Hu Ping, Yi Zhong Wu, and Li Ping Chen. "Data Driven Multivariate Adaptive Regression Splines Based Simulation Optimization." Applied Mechanics and Materials 44-47 (December 2010): 3800–3806. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.3800.

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This paper proposes a data driven based optimization approach which combines augmented Lagrangian method, MARS with effective data processing. In the approach, an expensive simulation run is required if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations have been performed. MARS is a self-adaptive regression process, which fits in with the multidimensional problems, and uses a modified recursive partitioning strategy to simplify high-dimensional problems into smaller yet highly accurate models. Combining the local response surface of MARS and augmented Lagrangian method improve sequential approximation optimization and reduce simulation times by effective data processing, yet maintain a low computational cost. The approach is applied to a six dimensional test function, a ten dimensional engineering problem and a two dimensional global test functions to demonstrate its feasibility and convergence, and yet some limiting properties.

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Alenezi, Fayadh, and K. C. Santosh. "Geometric Regularized Hopfield Neural Network for Medical Image Enhancement." International Journal of Biomedical Imaging 2021 (January 22, 2021): 1–12. http://dx.doi.org/10.1155/2021/6664569.

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One of the major shortcomings of Hopfield neural network (HNN) is that the network may not always converge to a fixed point. HNN, predominantly, is limited to local optimization during training to achieve network stability. In this paper, the convergence problem is addressed using two approaches: (a) by sequencing the activation of a continuous modified HNN (MHNN) based on the geometric correlation of features within various image hyperplanes via pixel gradient vectors and (b) by regulating geometric pixel gradient vectors. These are achieved by regularizing proposed MHNNs under cohomology, which enables them to act as an unconventional filter for pixel spectral sequences. It shifts the focus to both local and global optimizations in order to strengthen feature correlations within each image subspace. As a result, it enhances edges, information content, contrast, and resolution. The proposed algorithm was tested on fifteen different medical images, where evaluations were made based on entropy, visual information fidelity (VIF), weighted peak signal-to-noise ratio (WPSNR), contrast, and homogeneity. Our results confirmed superiority as compared to four existing benchmark enhancement methods.

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Ibraheem, Kais I., and Hisham M. Khudhur. "Optimization algorithm based on the Euler method for solving fuzzy nonlinear equations." Eastern-European Journal of Enterprise Technologies 1, no. 4 (115) (February 25, 2022): 13–19. http://dx.doi.org/10.15587/1729-4061.2022.252014.

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In a variety of engineering, scientific challenges, mathematics, chemistry, physics, biology, machine learning, deep learning, regression classification, computer science, programming, artificial intelligence, in the military, medical and engineering industries, robotics and smart cars, fuzzy nonlinear equations play a critical role. As a result, in this paper, an Optimization Algorithm based on the Euler Method approach for solving fuzzy nonlinear equations is proposed. In mathematics and computer science, the Euler approach (sometimes called the forward Euler method) is a first-order numerical strategy for solving ordinary differential equations (ODEs) with a specified initial value. The local error is proportional to the square of the step size, while the general error is proportional to the step size, according to the Euler technique. The Euler method is frequently used to create more complicated algorithms. The Optimization Algorithm Based on the Euler Method (OBE) uses the logic of slope differences, which is computed by the Euler approach for global optimizations as a search mechanism for promising logic. Furthermore, the mechanism of the proposed work takes advantage of two active phases: exploration and exploitation to find the most important promising areas within the distinct space and the best solutions globally based on a positive movement towards it. In order to avoid the solution of local optimal and increase the rate of convergence, we use the ESQ mechanism. The optimization algorithm based on the Euler method (OBE) is very efficient in solving fuzzy nonlinear equations and approaches the global minimum and avoids the local minimum. In comparison with the GWO algorithm, we notice a clear superiority of the OBE algorithm in reaching the solution with higher accuracy. We note from the numerical results that the new algorithm is 50 % superior to the GWO algorithm in Example 1, 51 % in Example 2 and 55 % in Example 3.

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Molero, J. M., E. M. Garzon, I. Garcia, and A. Plaza. "Analysis and Optimizations of Global and Local Versions of the RX Algorithm for Anomaly Detection in Hyperspectral Data." IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 6, no. 2 (April 2013): 801–14. http://dx.doi.org/10.1109/jstars.2013.2238609.

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Li, Wei, Huajun Gong, and Ruigang Yang. "Fast Texture Mapping Adjustment via Local/Global Optimization." IEEE Transactions on Visualization and Computer Graphics 25, no. 6 (June 1, 2019): 2296–303. http://dx.doi.org/10.1109/tvcg.2018.2831220.

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Xingping Dong, Jianbing Shen, Ling Shao, and Ming-Hsuan Yang. "Interactive Cosegmentation Using Global and Local Energy Optimization." IEEE Transactions on Image Processing 24, no. 11 (November 2015): 3966–77. http://dx.doi.org/10.1109/tip.2015.2456636.

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Pandini, D., L. T. Pileggi, and A. J. Strojwas. "Global and local congestion optimization in technology mapping." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 22, no. 4 (April 2003): 498–506. http://dx.doi.org/10.1109/tcad.2003.809646.

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Gergel, Victor, Vladimir Grishagin, and Ruslan Israfilov. "Local Tuning in Nested Scheme of Global Optimization." Procedia Computer Science 51 (2015): 865–74. http://dx.doi.org/10.1016/j.procs.2015.05.216.

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Kuiper, Jan H., Rik Huiskes, and Harrie Weinans. "Bone remodeling: comparing local adaptation and global optimization." Journal of Biomechanics 25, no. 7 (July 1992): 807. http://dx.doi.org/10.1016/0021-9290(92)90569-m.

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de Oliveira, Leonardo Correia, Silvana M. B. Afonso, and Bernardo Horowitz. "Global/local optimization strategies combined for waterflooding problems." Journal of the Brazilian Society of Mechanical Sciences and Engineering 38, no. 7 (December 21, 2015): 2051–62. http://dx.doi.org/10.1007/s40430-015-0461-y.

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Sergeyev, Yaroslav D. "An Information Global Optimization Algorithm with Local Tuning." SIAM Journal on Optimization 5, no. 4 (November 1995): 858–70. http://dx.doi.org/10.1137/0805041.

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Schnabel, Robert B. "Concurrent function evaluations in local and global optimization." Computer Methods in Applied Mechanics and Engineering 64, no. 1-3 (October 1987): 537–52. http://dx.doi.org/10.1016/0045-7825(87)90055-7.

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Gaviano, M., D. Lera, and A. M. Steri. "A local search method for continuous global optimization." Journal of Global Optimization 48, no. 1 (January 10, 2010): 73–85. http://dx.doi.org/10.1007/s10898-009-9519-7.

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Custódio, A. L., and J. F. A. Madeira. "GLODS: Global and Local Optimization using Direct Search." Journal of Global Optimization 62, no. 1 (August 13, 2014): 1–28. http://dx.doi.org/10.1007/s10898-014-0224-9.

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