Relevant bibliographies by topics / Nonconvex Sets

Academic literature on the topic 'Nonconvex Sets'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Nonconvex Sets"

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Cong, Chang, and Peibiao Zhao. "Non-Cash Risk Measure on Nonconvex Sets." Mathematics 6, no. 10 (October 1, 2018): 186. http://dx.doi.org/10.3390/math6100186.

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Monetary risk measures are interpreted as the smallest amount of external cash that must be added to a financial position to make the position acceptable. In this paper, A new concept: non-cash risk measure is proposed and this measure provides an approach to transform the unacceptable positions into the acceptable positions in a nonconvex set. Non-cash risk measure uses not only cash but also other kinds of assets to adjust the position. This risk measure is nonconvex due to the use of optimization problem in L 1 norm. A convex extension of the nonconvex risk measure is derived and the relationship between the convex extension and the non-cash risk measure is detailed.
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Blasi, Francesco S. de, Giulio Pianigiani, and Vasile Staicu. "On the solution sets of some nonconvex hyperbolic differential inclusions." Czechoslovak Mathematical Journal 45, no. 1 (1995): 107–16. http://dx.doi.org/10.21136/cmj.1995.128505.

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Panasyuk, A. I. "Differential equation for nonconvex attainment sets." Mathematical Notes of the Academy of Sciences of the USSR 37, no. 5 (May 1985): 395–400. http://dx.doi.org/10.1007/bf01157972.

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Chrétien, Stéphane, and Pascal Bondon. "Projection Methods for Uniformly Convex Expandable Sets." Mathematics 8, no. 7 (July 6, 2020): 1108. http://dx.doi.org/10.3390/math8071108.

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Many problems in medical image reconstruction and machine learning can be formulated as nonconvex set theoretic feasibility problems. Among efficient methods that can be put to work in practice, successive projection algorithms have received a lot of attention in the case of convex constraint sets. In the present work, we provide a theoretical study of a general projection method in the case where the constraint sets are nonconvex and satisfy some other structural properties. We apply our algorithm to image recovery in magnetic resonance imaging (MRI) and to a signal denoising in the spirit of Cadzow’s method.
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FLETCHER, JAMES, and WARREN B. MOORS. "CHEBYSHEV SETS." Journal of the Australian Mathematical Society 98, no. 2 (November 11, 2014): 161–231. http://dx.doi.org/10.1017/s1446788714000561.

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AbstractA Chebyshev set is a subset of a normed linear space that admits unique best approximations. In the first part of this paper we present some basic results concerning Chebyshev sets. In particular, we investigate properties of the metric projection map, sufficient conditions for a subset of a normed linear space to be a Chebyshev set, and sufficient conditions for a Chebyshev set to be convex. In the second half of the paper we present a construction of a nonconvex Chebyshev subset of an inner product space.
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Vinter, Richard B. "The Hamiltonian Inclusion for Nonconvex Velocity Sets." SIAM Journal on Control and Optimization 52, no. 2 (January 2014): 1237–50. http://dx.doi.org/10.1137/130917417.

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Park, S., and I. S. Kim. "Remarks on saddle points in nonconvex sets." Applied Mathematics Letters 13, no. 1 (January 2000): 111–13. http://dx.doi.org/10.1016/s0893-9659(99)00153-6.

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Drusvyatskiy, D., A. D. Ioffe, and A. S. Lewis. "Transversality and Alternating Projections for Nonconvex Sets." Foundations of Computational Mathematics 15, no. 6 (August 21, 2015): 1637–51. http://dx.doi.org/10.1007/s10208-015-9279-3.

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Clarke, F. H., Yu S. Ledyaev, and R. J. Stern. "Fixed points and equilibria in nonconvex sets." Nonlinear Analysis: Theory, Methods & Applications 25, no. 2 (July 1995): 145–61. http://dx.doi.org/10.1016/0362-546x(94)00215-4.

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Li, Guoyin, Chunming Tang, Gaohang Yu, and Zengxin Wei. "On a Separation Principle for Nonconvex Sets." Set-Valued Analysis 16, no. 7-8 (July 12, 2008): 851–60. http://dx.doi.org/10.1007/s11228-008-0099-3.

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Dissertations / Theses on the topic "Nonconvex Sets"

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Schaad, Jason. "Modeling the 8-queens problem and Sudoku using an algorithm based on projections onto nonconvex sets." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/28469.

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We begin with some basic definitions and concepts from convex analysis and projection onto convex sets (POCS). We next introduce various algorithms for converging to the intersection of convex sets and review various results (Elser’s Difference Map is equivalent to the Douglas-Rachford and Fienup’s Hybrid Input-Output algorithms which are both equivalent to the Hybrid Projection-Reflection algorithm). Our main contribution is two-fold. First, we show how to model the 8-queens problem and following Elser, we model Sudoku as well. In both cases we use several very nonconvex sets and while the theory for convex sets does not apply, so far the algorithm finds a solution. Second, we show that the operator governing the Douglas-Rachford iteration need not be a proximal map even when the two involved resolvents are; this refines an observation of Eckstein.
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洪有明. "Fixed point theorems for nonexpansive mappings in nonconvex sets." Thesis, 1992. http://ndltd.ncl.edu.tw/handle/31118759196651246481.

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Hesse, Robert. "Fixed Point Algorithms for Nonconvex Feasibility with Applications." Doctoral thesis, 2014. http://hdl.handle.net/11858/00-1735-0000-0022-5F3F-E.

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Books on the topic "Nonconvex Sets"

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Duality in nonconvex approximation and optimization. New York: Springer, 2005.

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V, Kalashnikov V., ed. Optimization with multivalued mappings: Theory, applications, and algorithms. New York: Springer, 2006.

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Singer, Ivan. Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics). Springer, 2006.

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Luderer, B., L. Minchenko, and T. Satsura. Multivalued Analysis and Nonlinear Programming Problems with Perturbations (Nonconvex Optimization and Its Applications). Springer, 2002.

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Dempe, Stephan, and Vyacheslav Kalashnikov. Optimization with Multivalued Mappings: Theory, Applications and Algorithms. Springer, 2010.

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Optimization with Multivalued Mappings: Theory, Applications and Algorithms. Springer London, Limited, 2006.

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Book chapters on the topic "Nonconvex Sets"

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Tuy, Hoang. "Convex Sets." In Nonconvex Optimization and Its Applications, 3–40. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2809-5_1.

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Pázman, Andrej. "Concentration Sets, Elfving Sets and Norms in Optimum Design." In Nonconvex Optimization and Its Applications, 101–12. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-3419-5_10.

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Mirkin, Boris. "Geometry of Data Sets." In Nonconvex Optimization and Its Applications, 59–107. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-0457-9_2.

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Dem’yanov, Vladimir F., Georgios E. Stavroulakis, Ludmila N. Polyakova, and Panagiotis D. Panagiotopoulos. "Quasidifferentiable Functions and Sets." In Nonconvex Optimization and Its Applications, 49–91. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4615-4113-4_2.

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Tuy, Hoang. "D.C. Functions and D.C. Sets." In Nonconvex Optimization and Its Applications, 83–105. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-2809-5_3.

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Rubinov, A. M. "Radiant Sets and Their Gauges." In Nonconvex Optimization and Its Applications, 235–61. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3137-8_10.

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Konno, Hiroshi, Phan Thien Thach, and Hoang Tuy. "D.C. Functions and D.C. Sets." In Nonconvex Optimization and Its Applications, 47–76. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-4098-4_3.

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Rapcsák, Tamás. "Fenchel’s Unsolved Problem of Level Sets." In Nonconvex Optimization and Its Applications, 253–70. Boston, MA: Springer US, 1997. http://dx.doi.org/10.1007/978-1-4615-6357-0_14.

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Pintér, János D. "Partition Methods on General Convex and Star Sets." In Nonconvex Optimization and Its Applications, 119–30. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4757-2502-5_8.

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Rubinov, Alexander. "Elements of Monotonic Analysis: IPH Functions and Normal Sets." In Nonconvex Optimization and Its Applications, 15–73. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-3200-9_2.

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Conference papers on the topic "Nonconvex Sets"

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Dabbene, Fabrizio, Constantino Lagoa, and Pavel Shcherbakov. "On the complexity of randomized approximations of nonconvex sets." In Control (MSC). IEEE, 2010. http://dx.doi.org/10.1109/cacsd.2010.5612656.

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Klodt, Lukas, Dominik Haumann, and Volker Willert. "Revisiting coverage control in nonconvex environments using visibility sets." In 2014 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2014. http://dx.doi.org/10.1109/icra.2014.6906593.

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Bhattiprolu, Vijay, Euiwoong Lee, and Assaf Naor. "A framework for quadratic form maximization over convex sets through nonconvex relaxations." In STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3406325.3451128.

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Chan, Ambrose, Elizabeth A. Croft, and James J. Little. "Modeling nonconvex workspace constraints from diverse demonstration sets for Constrained Manipulator Visual Servoing." In 2013 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2013. http://dx.doi.org/10.1109/icra.2013.6631002.

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Baab, C. T., J. C. Cockburn, H. A. Latchman, and D. Crisalle. "Extension of the Nyquist robust stability margin to systems with nonconvex value sets." In Proceedings of American Control Conference. IEEE, 2001. http://dx.doi.org/10.1109/acc.2001.945922.

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Gupta, Shuvomoy Das. "On Convergence of Heuristics Based on Douglas-Rachford Splitting and ADMM to Minimize Convex Functions over Nonconvex Sets†." In 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2018. http://dx.doi.org/10.1109/allerton.2018.8636076.

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Yang, Haoxuan, Kai Liu, Hua Wang, and Feiping Nie. "Learning Strictly Orthogonal p-Order Nonnegative Laplacian Embedding via Smoothed Iterative Reweighted Method." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/561.

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Laplacian Embedding (LE) is a powerful method to reveal the intrinsic geometry of high-dimensional data by using graphs. Imposing the orthogonal and nonnegative constraints onto the LE objective has proved to be effective to avoid degenerate and negative solutions, which, though, are challenging to achieve simultaneously because they are nonlinear and nonconvex. In addition, recent studies have shown that using the p-th order of the L2-norm distances in LE can find the best solution for clustering and promote the robustness of the embedding model against outliers, although this makes the optimization objective nonsmooth and difficult to efficiently solve in general. In this work, we study LE that uses the p-th order of the L2-norm distances and satisfies both orthogonal and nonnegative constraints. We introduce a novel smoothed iterative reweighted method to tackle this challenging optimization problem and rigorously analyze its convergence. We demonstrate the effectiveness and potential of our proposed method by extensive empirical studies on both synthetic and real data sets.
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Lo, Chihsiung, and Panos Y. Papalambros. "On Global Feasible Search for Global Design Optimization With Application to Generalized Polynomial Models." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0120.

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Abstract A powerful idea for deterministic global optimization is the use of global feasible search, namely, algorithms that guarantee finding feasible solutions of nonconvex problems or prove that none exists. In this article, a set of conditions for global feasible search algorithms is established. The utility of these conditions is demonstrated on two algorithms that solve special problem classes globally. Also, a new model transformation is shown to convert a generalized polynomial problem into one of the special classes above. A flywheel design example illustrates the approach. A sequel article provides further computational details and design examples.
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Ganter, M. A., and B. P. Isarankura. "Dynamic Collision Detection Using Space Partitioning." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0022.

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Abstract A technique termed space partitioning is employed which dramatically reduces the computation time required to detect dynamic collision during computer simulation. The simulated environment is composed of two nonconvex polyhedra traversing two general six degree of freedom trajectories. This space partitioning technique reduces collision detection time by subdividing the space containing a given object into a set of linear partitions. Using these partitions, all testing can be confined to the local region of overlap between the two objects. Further, all entities contained in the partitions inside the region of overlap are ordered based on their respective minimums and maximums to further reduce testing. Experimental results indicate a worst-case collision detection time for two one thousand faced objects is approximately three seconds per trajectory step.
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Smith, J. Cole, Alfonso Ortega, Colleen M. Gabel, and Dale Henderson. "Parameter Optimization for a Temperature Estimation Model." In ASME 2003 International Electronic Packaging Technical Conference and Exhibition. ASMEDC, 2003. http://dx.doi.org/10.1115/ipack2003-35254.

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We consider a problem arising in designing Compact Thermal Models (CTMs) for the purpose of simulating the thermal response of a package. CTMs are often preferred over more detailed models due to their minimal representation and the reduced computations required to obtain accurate nodal temperature predictions under hypothetical scenarios. The quality of CTM performance depends on the determination of an appropriate set of parameters that drive the model. The subject of this paper is a heuristic nonlinear optimization approach to computing the set of CTM parameters that best predicts the thermal response of a package. Our algorithm solves a series of one-dimensional nonconvex optimization problems to obtain these parameters, exploiting the special structure of the CTM in order to improve both the execution time of the algorithm and the quality of the CTM performance. We conclude the paper by providing a brief array of computational results as a proof of concept, along with several possible future research extensions.
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