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Journal articles on the topic 'Nonlinear robust optimization'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Leyffer, Sven, Matt Menickelly, Todd Munson, Charlie Vanaret, and Stefan M. Wild. "A survey of nonlinear robust optimization." INFOR: Information Systems and Operational Research 58, no. 2 (March 17, 2020): 342–73. http://dx.doi.org/10.1080/03155986.2020.1730676.

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2

Yuan, Yuan, Zukui Li, and Biao Huang. "Nonlinear robust optimization for process design." AIChE Journal 64, no. 2 (September 12, 2017): 481–94. http://dx.doi.org/10.1002/aic.15950.

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3

Zhang, Y. "General Robust-Optimization Formulation for Nonlinear Programming." Journal of Optimization Theory and Applications 132, no. 1 (February 16, 2007): 111–24. http://dx.doi.org/10.1007/s10957-006-9082-z.

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4

Diehl, Moritz, Hans Georg Bock, and Ekaterina Kostina. "An approximation technique for robust nonlinear optimization." Mathematical Programming 107, no. 1-2 (December 30, 2005): 213–30. http://dx.doi.org/10.1007/s10107-005-0685-1.

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5

Ben-Tal, Aharon, Ruud Brekelmans, Dick den Hertog, and Jean-Philippe Vial. "Globalized Robust Optimization for Nonlinear Uncertain Inequalities." INFORMS Journal on Computing 29, no. 2 (May 2017): 350–66. http://dx.doi.org/10.1287/ijoc.2016.0735.

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6

HEYNE, GREGOR, MICHAEL KUPPER, and LUDOVIC TANGPI. "PORTFOLIO OPTIMIZATION UNDER NONLINEAR UTILITY." International Journal of Theoretical and Applied Finance 19, no. 05 (July 29, 2016): 1650029. http://dx.doi.org/10.1142/s0219024916500291.

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This paper studies the utility maximization problem of an agent with nontrivial endowment, and whose preferences are modeled by the maximal subsolution of a backward stochastic differential equation (BSDE). We prove existence of an optimal trading strategy and relate our existence result to the existence of a maximal subsolution to a controlled decoupled forward–BSDE (FBSDE). Using BSDE duality, we show that the utility maximization problem can be seen as a robust control problem admitting a saddle point if the generator of the BSDE additionally satisfies a specific growth condition. We show by convex duality that any saddle point of the robust control problem agrees with a primal and a dual optimizer of the utility maximization problem, and can be characterized in terms of a BSDE solution.

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7

OISHI, Yasuaki. "501 Robust Control against Nonlinear Uncertainty : An Approach through Robust Optimization." Proceedings of Conference of Tokai Branch 2008.57 (2008): 349–50. http://dx.doi.org/10.1299/jsmetokai.2008.57.349.

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8

Ma, Bai, Wang, and Fang. "Robust Stereo Visual-Inertial Odometry Using Nonlinear Optimization." Sensors 19, no. 17 (August 29, 2019): 3747. http://dx.doi.org/10.3390/s19173747.

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The fusion of visual and inertial odometry has matured greatly due to the complementarity of the two sensors. However, the use of high-quality sensors and powerful processors in some applications is difficult due to size and cost limitations, and there are also many challenges in terms of robustness of the algorithm and computational efficiency. In this work, we present VIO-Stereo, a stereo visual-inertial odometry (VIO), which jointly combines the measurements of the stereo cameras and an inexpensive inertial measurement unit (IMU). We use nonlinear optimization to integrate visual measurements with IMU readings in VIO tightly. To decrease the cost of computation, we use the FAST feature detector to improve its efficiency and track features by the KLT sparse optical flow algorithm. We also incorporate accelerometer bias into the measurement model and optimize it together with other variables. Additionally, we perform circular matching between the previous and current stereo image pairs in order to remove outliers in the stereo matching and feature tracking steps, thus reducing the mismatch of feature points and improving the robustness and accuracy of the system. Finally, this work contributes to the experimental comparison of monocular visual-inertial odometry and stereo visual-inertial odometry by evaluating our method using the public EuRoC dataset. Experimental results demonstrate that our method exhibits competitive performance with the most advanced techniques.

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9

JAYARAMAN, BASKAR, and BRADLEY R. HOLT. "An optimization approach to robust nonlinear control design." International Journal of Control 59, no. 3 (March 1994): 639–64. http://dx.doi.org/10.1080/00207179408923098.

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10

Lee, Chang Jun, Vinay Prasad, and Jong Min Lee. "Stochastic Nonlinear Optimization for Robust Design of Catalysts." Industrial & Engineering Chemistry Research 50, no. 7 (April 6, 2011): 3938–46. http://dx.doi.org/10.1021/ie102103w.

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11

Houska, Boris, and Moritz Diehl. "Nonlinear robust optimization via sequential convex bilevel programming." Mathematical Programming 142, no. 1-2 (September 15, 2012): 539–77. http://dx.doi.org/10.1007/s10107-012-0591-2.

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12

Soleimanian, Azam, and Ghasemali Salmani Jajaei. "Robust nonlinear optimization with conic representable uncertainty set." European Journal of Operational Research 228, no. 2 (July 2013): 337–44. http://dx.doi.org/10.1016/j.ejor.2013.02.018.

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13

Milz, Johannes, and Michael Ulbrich. "An Approximation Scheme for Distributionally Robust Nonlinear Optimization." SIAM Journal on Optimization 30, no. 3 (January 2020): 1996–2025. http://dx.doi.org/10.1137/19m1263121.

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14

Luo, YaZhong, Zhen Yang, and HengNian Li. "Robust optimization of nonlinear impulsive rendezvous with uncertainty." Science China Physics, Mechanics and Astronomy 57, no. 4 (January 17, 2014): 731–40. http://dx.doi.org/10.1007/s11433-013-5295-y.

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15

Kastsian, Darya, and Martin Mönnigmann. "Robust optimization of periodically operated nonlinear uncertain processes." Chemical Engineering Science 106 (March 2014): 109–18. http://dx.doi.org/10.1016/j.ces.2013.11.023.

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16

Hübner, Jens, Martin Schmidt, and Marc C. Steinbach. "Optimization techniques for tree-structured nonlinear problems." Computational Management Science 17, no. 3 (February 5, 2020): 409–36. http://dx.doi.org/10.1007/s10287-020-00362-9.

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Abstract Robust model predictive control approaches and other applications lead to nonlinear optimization problems defined on (scenario) trees. We present structure-preserving Quasi-Newton update formulas as well as structured inertia correction techniques that allow to solve these problems by interior-point methods with specialized KKT solvers for tree-structured optimization problems. The same type of KKT solvers could be used in active-set based SQP methods. The viability of our approach is demonstrated by two robust control problems.

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17

Wang, Lei, Xing Wang, and Nan-jing Huang. "Tractable Approximation to Robust Nonlinear Production Frontier Problem." Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/965835.

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Robust optimization is a rapidly developing methodology for handling optimization problems affected by the uncertain-but-bounded data perturbations. In this paper, we consider the nonlinear production frontier problem where the traditional expected linear cost minimization objective is replaced by one that explicitly addresses cost variability. We propose a robust counterpart for the nonlinear production frontier problem that preserves the computational tractability of the nominal problem. We also provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions.

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18

Gally, Tristan, Christopher M. Gehb, Philip Kolvenbach, Anja Kuttich, Marc E. Pfetsch, and Stefan Ulbrich. "Robust Truss Topology Design with Beam Elements via Mixed Integer Nonlinear Semidefinite Programming." Applied Mechanics and Materials 807 (November 2015): 229–38. http://dx.doi.org/10.4028/www.scientific.net/amm.807.229.

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In this article, we propose a nonlinear semidefinite program (SDP) for the robust trusstopology design (TTD) problem with beam elements. Starting from the semidefinite formulation ofthe robust TTD problem we derive a stiffness matrix that can model rigid connections between beams.Since the stiffness matrix depends nonlinearly on the cross-sectional areas of the beams, this leads toa nonlinear SDP. We present numerical results using a sequential SDP approach and compare them toresults obtained via a general method for robust PDE-constrained optimization applied to the equationsof linear elasticity. Furthermore, we present two mixed integer semidefinite programs (MISDP), onefor the optimal choice of connecting elements, which is nonlinear, and one for the correspondingproblem with discrete cross-sectional areas.

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19

Mou, Wei, Han Wang, and Gerald Seet. "Robust Homography Estimation Based on Nonlinear Least Squares Optimization." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/897050.

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The homography between image pairs is normally estimated by minimizing a suitable cost function given 2D keypoint correspondences. The correspondences are typically established using descriptor distance of keypoints. However, the correspondences are often incorrect due to ambiguous descriptors which can introduce errors into following homography computing step. There have been numerous attempts to filter out these erroneous correspondences, but it is unlikely to always achieve perfect matching. To deal with this problem, we propose a nonlinear least squares optimization approach to compute homography such that false matches have no or little effect on computed homography. Unlike normal homography computation algorithms, our method formulates not only the keypoints’ geometric relationship but also their descriptor similarity into cost function. Moreover, the cost function is parametrized in such a way that incorrect correspondences can be simultaneously identified while the homography is computed. Experiments show that the proposed approach can perform well even with the presence of a large number of outliers.

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20

Ball, Joseph A., Jerawan Chudoung, and Martin V. Day. "Robust Optimal Switching Control for Nonlinear Systems." SIAM Journal on Control and Optimization 41, no. 3 (January 2002): 900–931. http://dx.doi.org/10.1137/s0363012900372611.

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21

James, M. R., M. C. Smith, and G. Vinnicombe. "Gap Metrics, Representations, and Nonlinear Robust Stability." SIAM Journal on Control and Optimization 43, no. 5 (January 2005): 1535–82. http://dx.doi.org/10.1137/s0363012901393067.

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22

Wang, M., ZB Sun, BC Zhang, ZX Pang, and DW Jiang. "A Dai–Yuan conjugate gradient algorithm of linear equation constrained optimization approach for optimal robust controller of bipedal robots." International Journal of Advanced Robotic Systems 17, no. 1 (January 1, 2020): 172988141989017. http://dx.doi.org/10.1177/1729881419890178.

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In this article, combined rapidly exponential control Lyapunov function with hybrid zero dynamics, a sufficiently descent projected Dai–Yuan approach is proposed, investigated, and analyzed for online solving optimal robust control problems with linear equation constraints of bipedal robots. Moreover, a new approach is developed for designing optimal robust controller. To demonstrate the effectiveness and feasibility of the proposed method, we will conduct numerical simulations on the model of three-link robot with nonlinear, impulsive, and under-actuated dynamics. Numerical results show that the bipedal robot can walk effectively and stability on the ground though the optimal robust controller when the parameters of the hybrid system model are disturbed three times. Furthermore, under the random noise condition, the bipedal robot can walk stably and effectively through online computing the nonlinear optimization problem for optimal robust controller. In addition, some classical control methods are compared with the developed approach in this article, numerical results are reported and analyzed to substantiate the feasibility and superiority of the proposed method for linear equation constrained optimization problem. Last, this article develops a systematic approach on exploiting optimal robust control technique to design hybrid system models for robustly and accurately via online solving linear equation constrained optimization problems.

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23

Silva, A. D. G., A. A. Cavalini Jr, and V. Steffen Jr. "Fuzzy Robust Design of Dynamic Vibration Absorbers." Shock and Vibration 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/2081518.

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This paper is dedicated to the development of robust optimization and decision making techniques taking into account the uncertain parameters of linear and nonlinear dynamic vibration absorbers. In this case, novel approaches are proposed regarding different fuzzy logic optimization strategies. The uncertain parameters of the considered mechanical systems are treated as fuzzy variables. Consequently, the associated optimization problem is described as a fuzzy function that maps the fuzzy inputs. The proposed techniques are applied to the design of dynamic vibration absorbers. This numerical study illustrates the versatility and convenience of the proposed fuzzy logic optimization strategies.

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24

Bouzbida, Mohamed, Lassad Hassine, and Abdelkader Chaari. "Robust Kernel Clustering Algorithm for Nonlinear System Identification." Mathematical Problems in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/2427309.

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In engineering field, it is necessary to know the model of the real nonlinear systems to ensure its control and supervision; in this context, fuzzy modeling and especially the Takagi-Sugeno fuzzy model has drawn the attention of several researchers in recent decades owing to their potential to approximate nonlinear behavior. To identify the parameters of Takagi-Sugeno fuzzy model several clustering algorithms are developed such as the Fuzzy C-Means (FCM) algorithm, Possibilistic C-Means (PCM) algorithm, and Possibilistic Fuzzy C-Means (PFCM) algorithm. This paper presents a new clustering algorithm for Takagi-Sugeno fuzzy model identification. Our proposed algorithm called Robust Kernel Possibilistic Fuzzy C-Means (RKPFCM) algorithm is an extension of the PFCM algorithm based on kernel method, where the Euclidean distance used the robust hyper tangent kernel function. The proposed algorithm can solve the nonlinear separable problems found by FCM, PCM, and PFCM algorithms. Then an optimization method using the Particle Swarm Optimization (PSO) method combined with the RKPFCM algorithm is presented to overcome the convergence to a local minimum of the objective function. Finally, validation results of examples are given to demonstrate the effectiveness, practicality, and robustness of our proposed algorithm in stochastic environment.

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25

TANG, ZHILI. "UNCERTAINTY BASED ROBUST OPTIMIZATION IN AERODYNAMICS." Modern Physics Letters B 23, no. 03 (January 30, 2009): 477–80. http://dx.doi.org/10.1142/s0217984909018692.

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The Taguchi robust design concept is combined with the multi-objective deterministic optimization method to overcome single point design problems in Aerodynamics. Starting from a statistical definition of stability, the method finds, Nash equilibrium solutions for performance and its stability simultaneously.

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26

Cervera, Joaquín, and Alfonso Baños. "Nonlinear Nonconvex Optimization by Evolutionary Algorithms Applied to Robust Control." Mathematical Problems in Engineering 2009 (2009): 1–21. http://dx.doi.org/10.1155/2009/671869.

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This work focuses on the problem of automatic loop shaping in the context of robust control. More specifically in the framework given by Quantitative Feedback Theory (QFT), traditionally the search of an optimum design, a non convex and nonlinear optimization problem, is simplified by linearizing and/or convexifying the problem. In this work, the authors propose a suboptimal solution using a fixed structure in the compensator and evolutionary optimization. The main idea in relation to previous work consists of the study of the use of fractional compensators, which give singular properties to automatically shape the open loop gain function with a minimum set of parameters, which is crucial for the success of evolutionary algorithms. Additional heuristics are proposed in order to guide evolutionary process towards close to optimum solutions, focusing on local optima avoidance.

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27

Galvan-Perez, Daniel, Hugo Yañez-Badillo, Francisco Beltran-Carbajal, Ivan Rivas-Cambero, Antonio Favela-Contreras, and Ruben Tapia-Olvera. "Neural Adaptive Robust Motion-Tracking Control for Robotic Manipulator Systems." Actuators 11, no. 9 (September 7, 2022): 255. http://dx.doi.org/10.3390/act11090255.

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This paper deals with the motion trajectory tracking control problem based on output feedback and artificial neural networks for anthropomorphic manipulator robots under disturbed operating scenarios. This class of manipulator robots constitutes nonlinear dynamic systems subjected to disturbance torques induced mainly by work payload. Parametric uncertainty and possible dynamic modeling errors stand for other kind of disturbances that can deteriorate the efficiency and robustness of the tracking of controlled nonlinear robotic system trajectories. In fact, the presence of unknown dynamic disturbances is unavoidable in industrial robotic engineering systems. Therefore, for high-precision applications, such as laser cutting, marking, or welding, effective control schemes should be designed to guarantee adequate motion profile tracking planned on this class of disturbed nonlinear robotic system. In this context, a new adaptive robust motion trajectory tracking control scheme based on output feedback and artificial neural networks of anthropomorphic manipulator robots is presented. Three-layer B-spline artificial neural networks and time-series modeling are properly exploited in the design of novel adaptive robust motion tracking controllers for robotic applications of laser manufacturing. In this way, dependency on detailed nonlinear mathematical modeling of robotic systems is considerably reduced, and real-time estimation of uncertain dynamic disturbances is not required. Furthermore, several cases studies to demonstrate the motion planning tracking control robustness for a class of MIMO nonlinear robotic systems are described. blue Insights for the extension of the introduced output-feedback adaptive neural control design approach for other architecture of nonlinear robotic systems are depicted.

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28

Zhang, Jiaxu, Shiying Zhou, Fengjun Li, and Jian Zhao. "Integrated nonlinear robust adaptive control for active front steering and direct yaw moment control systems with uncertainty observer." Transactions of the Institute of Measurement and Control 42, no. 16 (August 31, 2020): 3267–80. http://dx.doi.org/10.1177/0142331220949718.

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This paper presents an integrated nonlinear robust adaptive controller with uncertainty observer for active front wheel steering system and direct yaw moment control system. First, an integrated vehicle chassis control model is established as the nominal model with the additive and multiplicative uncertainties of the system. Secondly, an integrated nonlinear robust adaptive control law with the additive uncertainty observer is designed via Lyapunov stability theory to calculate the corrective yaw moment, and an adaptive law is designed based on projection correction method to online estimate and compensate the multiplicative uncertainty of the system. Then, the constrained optimal allocation problem of the corrective yaw moment is transformed into the nonlinear optimization problem, and the sequential quadratic programming method is used to solve the nonlinear optimization problem to coordinate active front wheel steering system and direct yaw moment control system. Finally, the performance of the proposed integrated nonlinear robust adaptive controller is verified via vehicle dynamics simulation software.

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29

Abbaszadeh, Masoud, and Horacio J. Marquez. "Robust H-Filtering for Lipschitz Nonlinear Systems via Multiobjective Optimization." Journal of Signal and Information Processing 01, no. 01 (2010): 24–34. http://dx.doi.org/10.4236/jsip.2010.11003.

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30

Tang, Jiachang, Chunming Fu, Chengji Mi, and Haibo Liu. "An interval sequential linear programming for nonlinear robust optimization problems." Applied Mathematical Modelling 107 (July 2022): 256–74. http://dx.doi.org/10.1016/j.apm.2022.02.037.

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31

Harms, R. L., F. J. Fritz, A. Tobisch, R. Goebel, and A. Roebroeck. "Robust and fast nonlinear optimization of diffusion MRI microstructure models." NeuroImage 155 (July 2017): 82–96. http://dx.doi.org/10.1016/j.neuroimage.2017.04.064.

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32

Takeda, A., S. Taguchi, and R. H. Tütüncü. "Adjustable Robust Optimization Models for a Nonlinear Two-Period System." Journal of Optimization Theory and Applications 136, no. 2 (October 26, 2007): 275–95. http://dx.doi.org/10.1007/s10957-007-9288-8.

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33

Treanţă, Savin, and Tareq Saeed. "Duality Results for a Class of Constrained Robust Nonlinear Optimization Problems." Mathematics 11, no. 1 (December 29, 2022): 192. http://dx.doi.org/10.3390/math11010192.

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In this paper, we establish various results of duality for a new class of constrained robust nonlinear optimization problems. For this new class of problems, involving functionals of (path-independent) curvilinear integral type and mixed constraints governed by partial derivatives of second order and uncertain data, we formulate and study Wolfe, Mond-Weir and mixed type robust dual optimization problems. In this regard, by considering the concept of convex curvilinear integral vector functional, determined by controlled second-order Lagrangians including uncertain data, and the notion of robust weak efficient solution associated with the considered problem, we create a new mathematical context to state and prove the duality theorems. Furthermore, an illustrative application is presented.

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34

Borges, R. A., A. M. G. de Lima, and V. Steffen Jr. "Robust Optimal Design of a Nonlinear Dynamic Vibration Absorber Combining Sensitivity Analysis." Shock and Vibration 17, no. 4-5 (2010): 507–20. http://dx.doi.org/10.1155/2010/587502.

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Dynamic vibration absorbers are discrete devices developed in the beginning of the last century used to attenuate the vibrations of different engineering structures. They have been used in several engineering applications, such as ships, power lines, aeronautic structures, civil engineering constructions subjected to seismic induced excitations, compressor systems, etc. However, in the context of nonlinear dynamics, few works have been proposed regarding the robust optimal design of nonlinear dynamic vibration absorbers. In this paper, a robust optimization strategy combined with sensitivity analysis of systems incorporating nonlinear dynamic vibration absorbers is proposed. Although sensitivity analysis is a well known numerical technique, the main contribution intended for this study is its extension to nonlinear systems. Due to the numerical procedure used to solve the nonlinear equations, the sensitivities addressed herein are computed from the first-order finite-difference approximations. With the aim of increasing the efficiency of the nonlinear dynamic absorber into a frequency band of interest, and to augment the robustness of the optimal design, a robust optimization strategy combined with the previous sensitivities is addressed. After presenting the underlying theoretical foundations, the proposed robust design methodology is performed for a two degree-of-freedom system incorporating a nonlinear dynamic vibration absorber. Based on the obtained results, the usefulness of the proposed methodology is highlighted.

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35

Sun, Guanglei, Youlin Shang, and Roxin Zhang. "An Efficient and Robust Improved Whale Optimization Algorithm for Large Scale Global Optimization Problems." Electronics 11, no. 9 (May 4, 2022): 1475. http://dx.doi.org/10.3390/electronics11091475.

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As an efficient meta-heuristic algorithm, the whale optimization algorithm (WOA) has been extensively applied to practical problems. However, WOA still has the drawbacks of converging slowly, and jumping out from extreme points especially for large scale optimization problems. To overcome these defects, a modified whale optimization algorithm integrated with a crisscross optimization algorithm (MWOA-CS) is proposed. In MWOA-CS, each dimension of the optimization problem updates its position by randomly performing improved WOA or crisscross optimization algorithm during the entire iterative process. The improved WOA adopts the new nonlinear convergence factor and nonlinear inertia weight to tune the ability of exploitation and exploration. To analyze the performance of MWOA-CS, a series of numerical experiments were performed on 30 test benchmark functions with dimension ranging from 300 to 1000. The experimental results revealed that the presented MWOA-CS provided better convergence speed and accuracy, and meanwhile, displayed a significantly more effective and robust performance than the original WOA and other state of the art meta-heuristic algorithms for solving large scale global optimization problems.

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36

Zhao, Jia Cheng, Cheng Li Su, and Ping Li. "Robust Predictive Control for Uncertain Time-Delay Systems with Nonlinear Disturbance." Advanced Materials Research 490-495 (March 2012): 1496–500. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.1496.

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Based on predictive control principle of receding optimization, the infinite time domain “min-max” optimization problems are converted into convex programming problems by Lyapunov stable theory and linear matrix inequality (LMI). The sufficient conditions for the robust stability of the uncertain time-delay system are given. Finally, the simulation results illustrate the effectiveness of the proposed methods.

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37

Hassan, L., A. Zemouche, and M. Boutayeb. "Robust Unknown Input Observers for Nonlinear Time-Delay Systems." SIAM Journal on Control and Optimization 51, no. 4 (January 2013): 2735–52. http://dx.doi.org/10.1137/11085181x.

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38

Chen, C., G. Li, and A. C. C. Reynolds. "Robust Constrained Optimization of Short- and Long-Term Net Present Value for Closed-Loop Reservoir Management." SPE Journal 17, no. 03 (June 7, 2012): 849–64. http://dx.doi.org/10.2118/141314-pa.

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Summary In this paper, we develop an efficient algorithm for production optimization under linear and nonlinear constraints and an uncertain reservoir description. The linear and nonlinear constraints are incorporated into the objective function using the augmented Lagrangian method, and the bound constraints are enforced using a gradient-projection trust-region method. Robust long-term optimization maximizes the expected life-cycle net present value (NPV) over a set of geological models, which represent the uncertainty in reservoir description. Because the life-cycle optimal controls may be in conflict with the operator's objective of maximizing short-time production, the method is adapted to maximize the expectation of short-term NPV over the next 1 or 2 years subject to the constraint that the life-cycle NPV will not be substantially decreased. The technique is applied to synthetic reservoir problems to demonstrate its efficiency and robustness. Experiments show that the field cannot always achieve the optimal NPV using the optimal well controls obtained on the basis of a single but uncertain reservoir model, whereas the application of robust optimization reduces this risk significantly. Experimental results also show that robust sequential optimization on each short-term period is not able to achieve an expected life-cycle NPV as high as that obtained with robust long-term optimization.

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39

Liu, Zhe, and Albert C. Reynolds. "A Sequential-Quadratic-Programming-Filter Algorithm with a Modified Stochastic Gradient for Robust Life-Cycle Optimization Problems with Nonlinear State Constraints." SPE Journal 25, no. 04 (April 8, 2020): 1938–63. http://dx.doi.org/10.2118/193925-pa.

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Summary Solving a large-scale optimization problem with nonlinear state constraints is challenging when adjoint gradients are not available for computing the derivatives needed in the basic optimization algorithm used. Here, we present a methodology for the solution of an optimization problem with nonlinear and linear constraints, where the true gradients that cannot be computed analytically are approximated by ensemble-based stochastic gradients using an improved stochastic simplex approximate gradient (StoSAG). Our discussion is focused on the application of our procedure to waterflooding optimization where the optimization variables are the well controls and the cost function is the life-cycle net present value (NPV) of production. The optimization algorithm used for solving the constrained-optimization problem is sequential quadratic programming (SQP) with constraints enforced using the filter method. We introduce modifications to StoSAG that improve its fidelity [i.e., the improvements give a more accurate approximation to the true gradient (assumed here to equal the gradient computed with the adjoint method) than the approximation obtained using the original StoSAG algorithm]. The modifications to StoSAG vastly improve the performance of the optimization algorithm; in fact, we show that if the basic StoSAG is applied without the improvements, then the SQP might yield a highly suboptimal result for optimization problems with nonlinear state constraints. For robust optimization, each constraint should be satisfied for every reservoir model, which is highly computationally intensive. However, the computationally viable alternative of letting the reservoir simulation enforce the nonlinear state constraints using its internal heuristics yields significantly inferior results. Thus, we develop an alternative procedure for handling nonlinear state constraints, which avoids explicit enforcement of nonlinear constraints for each reservoir model yet yields results where any constraint violation for any model is extremely small.

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40

Chakraborty, Souvik, Sourav Das, and Solomon Tesfamariam. "Robust design optimization of nonlinear energy sink under random system parameters." Probabilistic Engineering Mechanics 65 (July 2021): 103139. http://dx.doi.org/10.1016/j.probengmech.2021.103139.

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41

Bukhari, H. J. "Robust optimization of a quartic multimodal nonlinear function - Methods and results." Journal of Information and Optimization Sciences 40, no. 3 (March 28, 2019): 767–88. http://dx.doi.org/10.1080/02522667.2018.1501922.

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42

Hsiao, Feng‐Hsiag, and Bor‐Sen Chen. "The robust optimization of multivariable systems with time‐varying nonlinear perturbations." Journal of the Chinese Institute of Engineers 10, no. 3 (April 1987): 317–27. http://dx.doi.org/10.1080/02533839.1987.9676977.

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43

Li, Yi, Shengxi Zhou, and Grzegorz Litak. "Robust design optimization of a nonlinear monostable energy harvester with uncertainties." Meccanica 55, no. 9 (July 24, 2020): 1753–62. http://dx.doi.org/10.1007/s11012-020-01216-z.

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van Dijk, N. P., M. Langelaar, and F. van Keulen. "Element deformation scaling for robust geometrically nonlinear analyses in topology optimization." Structural and Multidisciplinary Optimization 50, no. 4 (August 21, 2014): 537–60. http://dx.doi.org/10.1007/s00158-014-1145-4.

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Zhang, Ju-liang. "A robust trust region method for nonlinear optimization with inequality constraint." Applied Mathematics and Computation 176, no. 2 (May 2006): 688–99. http://dx.doi.org/10.1016/j.amc.2005.10.015.

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TU, MAAN-HUANG, CHIH-MIN LIN, and YU-PING LIN. "Robust optimization of multivariable feedback systems with time-varying nonlinear uncertainties." International Journal of Systems Science 24, no. 3 (March 1993): 599–608. http://dx.doi.org/10.1080/00207729308949509.

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Zhu, Qidan, Yu Han, Peng Liu, Yao Xiao, Peng Lu, and Chengtao Cai. "Motion Planning of Autonomous Mobile Robot Using Recurrent Fuzzy Neural Network Trained by Extended Kalman Filter." Computational Intelligence and Neuroscience 2019 (January 29, 2019): 1–16. http://dx.doi.org/10.1155/2019/1934575.

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This paper proposes a novel motion planning method for an autonomous ground mobile robot to address dynamic surroundings, nonlinear program, and robust optimization problems. A planner based on the recurrent fuzzy neural network (RFNN) is designed to program trajectory and motion of mobile robots to reach target. And, obstacle avoidance is achieved. In RFNN, inference capability of fuzzy logic and learning capability of neural network are combined to improve nonlinear programming performance. A recurrent frame with self-feedback loops in RFNN enhances stability and robustness of the structure. The extended Kalman filter (EKF) is designed to train weights of RFNN considering the kinematic constraint of autonomous mobile robots as well as target and obstacle constraints. EKF’s characteristics of fast convergence and little limit in training data make it suitable to train the weights in real time. Convergence of the training process is also analyzed in this paper. Optimization technique and update strategy are designed to improve the robust optimization of a system in dynamic surroundings. Simulation experiment and hardware experiment are implemented to prove the effectiveness of the proposed method. Hardware experiment is carried out on a tracked mobile robot. An omnidirectional vision is used to locate the robot in the surroundings. Forecast improvement of the proposed method is then discussed at the end.

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Chen, Y. H., and J. S. Chen. "Robust Composite Control for Singularly Perturbed Systems With Time-Varying Uncertainties." Journal of Dynamic Systems, Measurement, and Control 117, no. 4 (December 1, 1995): 445–52. http://dx.doi.org/10.1115/1.2801099.

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A two-time-scale linear system with uncertain time-varying parameter is to be stabilized. A class of robust composite controls is proposed. The control renders the system practically stable regardless of the true value of the parameter. The control scheme consists of linear and nonlinear parts. The linear part is designed via a two-level optimization setting. No matching condition is needed for the linear control. The nonlinear part is of continuous saturation type. Matching condition is needed for the nonlinear control. However, it can be achieved by choosing the boundary layer model appropriately.

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Zhao, Jing, and Maojun Bin. "Karush-Kuhn-Tucker optimality conditions for a class of robust optimization problems with an interval-valued objective function." Open Mathematics 18, no. 1 (July 22, 2020): 781–93. http://dx.doi.org/10.1515/math-2020-0042.

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Abstract In this article, we study the nonlinear and nonsmooth interval-valued optimization problems in the face of data uncertainty, which are called interval-valued robust optimization problems (IVROPs). We introduce the concept of nondominated solutions for the IVROP. If the interval-valued objective function f and constraint functions {g}_{i} are nonsmooth on Banach space E, we establish a nonsmooth and robust Karush-Kuhn-Tucker optimality theorem.

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Mehmood, Khizer, Naveed Ishtiaq Chaudhary, Zeshan Aslam Khan, Khalid Mehmood Cheema, Muhammad Asif Zahoor Raja, Ahmad H. Milyani, and Abdullah Ahmed Azhari. "Nonlinear Hammerstein System Identification: A Novel Application of Marine Predator Optimization Using the Key Term Separation Technique." Mathematics 10, no. 22 (November 11, 2022): 4217. http://dx.doi.org/10.3390/math10224217.

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The mathematical modelling and optimization of nonlinear problems arising in diversified engineering applications is an area of great interest. The Hammerstein structure is widely used in the modelling of various nonlinear processes found in a range of applications. This study investigates the parameter optimization of the nonlinear Hammerstein model using the abilities of the marine predator algorithm (MPA) and the key term separation technique. MPA is a population-based metaheuristic inspired by the behavior of predators for catching prey, and utilizes Brownian/Levy movement for predicting the optimal interaction between predator and prey. A detailed analysis of MPA is conducted to verify the accurate and robust behavior of the optimization scheme for nonlinear Hammerstein model identification.

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