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Ergodic Approach to Robust Optimization and infinite programming Problems

SET-VALUED AND VARIATIONAL ANALYSIS 2021年第2期29卷 409-423页

作者： Perez-Aros, Pedro Univ OHiggins Inst Ciencias Ingn Libertador Bernardo OHiggins 611 Rancagua Region Del Libe Chile

In this work, we show the consistency of an approach for solving robust optimization problems using sequences of sub-problems generated by ergodic measure preserving transformations. The main result of this paper is that the minimizers and the optimal value of the sub-problems converge, in some sense, to the minimizers and the optimal value of the initial problem, respectively. Our result particularly implies the consistency of the scenario approach for nonconvex optimization problems. Finally, we show that our method can also be used to solve infinite programming problems.

关键词： Stochastic optimization Scenario approach Robust optimization infinite programming Epi-convergence Ergodic theorems

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Optimality conditions for nonlinear infinite programming problems

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OPTIMIZATION LETTERS 2015年第6期9卷 1131-1147页

作者： de Oliveira, Valeriano A. dos Santos, Lucelina B. Osuna-Gomez, Rafaela Rojas-Medar, Marko A. UNESP Univ Estadual Paulista Inst Biociencias Letras & Ciencias Exatas BR-15054000 Sao Jose Do Rio Preto SP Brazil Univ Fed Parana Dept Matemat Ctr Politecn Setor Ciencias Exatas BR-81531990 Curitiba Parana Brazil Univ Seville Dept Estadist & Invest Operat Fac Matemat E-41012 Seville Spain Univ Bio Bio Fac Ciencias Dept Ciencias Basicas GMA Chillan Chile

An infinite programming problem consists in minimizing a functional defined on a real Banach space under an infinite number of constraints. The main purpose of this article is to provide sufficient conditions of optimality under generalized convexity assumptions. Such conditions are necessarily satisfied when the problem possesses the property that every stationary point is a global minimizer.

关键词： Nonlinear programming infinite programming Sufficient conditions Generalized convexity

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Optimality Conditions in DC-Constrained Mathematical programming Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2023年第3期198卷 1191-1225页

作者： Correa, Rafael Lopez, Marco A. Perez-Aros, Pedro Univ OHiggins Rancagua Chile Univ Chile DIM CMM Santiago Chile Univ Alicante Dept Math Alicante 03071 Spain Federat Univ Australia Ctr Informat & Appl Optimizat Ballarat Australia Univ OHiggins Inst Ciencias Ingn Rancagua Chile

This paper provides necessary and sufficient optimality conditions for abstract-constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of certain mappings, in particular their structure as difference of convex functions, and uses techniques of generalized differentiation (subdifferential and coderivative). It turns out that these tools can be used fruitfully out of the scope of Asplund spaces. Applications to infinite, stochastic and semi-definite programming are developed in separate sections.

关键词： DC functions DC-constrained programming Conic programming infinite programming Stochastic programming Semi-definite programming Supremum function

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Simultaneous Trajectory Optimization and Contact Selection for Contact-Rich Manipulation With High-Fidelity Geometry

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IEEE TRANSACTIONS ON ROBOTICS 2025年 41卷 2677-2690页

作者： Zhang, Mengchao Jha, Devesh K. Raghunathan, Arvind U. Hauser, Kris Univ Illinois Dept Mech Sci & Engn Urbana IL 61801 USA Mitsubishi Elect Res Labs MERL Cambridge MA 02139 USA Univ Illinois Sch Comp & Data Sci Urbana IL 61801 USA

Contact-implicit trajectory optimization (CITO) is an effective method to plan complex trajectories for various contact-rich systems including manipulation and locomotion. CITO formulates a mathematical program with complementarity constraints (MPCC) that enforces that contact forces must be zero when points are not in contact. However, MPCC solve times increase steeply with the number of allowable points of contact, which limits CITO's applicability to problems in which only a few, simple geometries are allowed us to make contact. This article introduces simultaneous trajectory optimization and contact selection (STOCS), as an extension of CITO that overcomes this limitation. The innovation of STOCS is to identify salient contact points and times inside the iterative trajectory optimization process. This effectively reduces the number of variables and constraints in each MPCC invocation. The STOCS framework, instantiated with key contact identification subroutines, renders the optimization of manipulation trajectories computationally tractable even for high-fidelity geometries consisting of tens of thousands of vertices.

关键词： infinite programming manipulation planning trajectory optimization trajectory optimization trajectory optimization

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A modified exchange algorithm for distributional robust optimization and applications in risk management

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2022年第1期29卷 130-157页

作者： Sun, Hailin Zhang, Dali Wu, Soon-Yi Chen, Liang Nanjing Normal Univ Sch Math Sci Jiangsu Key Lab NSLSCS Nanjing 210023 Peoples R China Shanghai Jiao Tong Univ Antai Coll Econ & Management Shanghai 200030 Peoples R China Natl Cheng Kung Univ Dept Math Tainan 70101 Taiwan Hunan Univ Coll Math & Econometr Changsha 410082 Hunan Peoples R China

Convex semi-definite semi-infinite programming problems (SDSIP) represent a special class of distributionally robust optimization (DRO) problems with a wide range of applications in engineering and economics. In this paper, we propose a modified exchange algorithm for convex SDSIP that arises from DRO with matrix moment constraints. We first explore the convergence results of the modified exchange algorithm and perform the efficiency analysis based on a set of benchmark tests. In addition, we apply the SDSIP framework to investigate an optimized certainty bound risk with an ambiguity uncertainty set and implement the algorithm to solve a practical risk minimization problem in portfolio selection. The empirical results show both the efficiency of the algorithm and the robustness of the risk measure.

关键词： semi‐ definite semi‐ infinite programming exchange method distributionally robust optimization convergence analysis worst optimized certainty equivalent risk

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Subdifferential of Optimal Value Functions in Nonlinear infinite programming

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APPLIED MATHEMATICS AND OPTIMIZATION 2012年第1期65卷 91-109页

作者： Huy, N. Q. Giang, N. D. Yao, J. -C. Hanoi Pedag Univ 2 Dept Math Vinh Phuc Vietnam Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 804 Taiwan

This paper presents an exact formula for computing the normal cones of the constraint set mapping including the Clarke normal cone and the Mordukhovich normal cone in infinite programming under the extended Mangasarian-Fromovitz constraint qualification condition. Then, we derive an upper estimate as well as an exact formula for the limiting subdifferential of the marginal/optimal value function in a general Banach space setting.

关键词： Variational analysis infinite programming Optimal value function Mangasarian-Fromovitz condition Normal cone Subdifferential

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Exact estimates of regularity modulus for infinite programming

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MATHEMATICAL programming 2010年第1期123卷 253-263页

作者： Sekiguchi, Yoshiyuki Tokyo Univ Marine Sci & Technol Fac Marine Technol Koto Ku Tokyo Japan

An exact estimate on the modulus of metric regularity for linear systems is given. By applying the estimate, we obtain explicit forms of the modulus for linear conical systems and differentiable nonlinear systems on t... 详细信息

关键词： Modulus of metric regularity infinite programming

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infinite kernel learning via infinite and semi-infinite programming

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OPTIMIZATION METHODS & SOFTWARE 2010年第6期25卷 937-970页

作者： Ozour-Akyuz, S. Weber, G. -W. Bahcesehir Univ Dept Math & Comp Sci Istanbul Turkey Middle E Tech Univ Inst Appl Math TR-06531 Ankara Turkey Univ Siegen Fac Econ Management Sci & Law Siegen Germany

As data become heterogeneous, multiple kernel learning methods may help to classify them. To overcome the drawback lying in its (multiple) finite choice, we propose a novel method of 'infinite' kernel combinations for learning problems with the help of infinite and semi-infinite optimizations. Looking at all the infinitesimally fine convex combinations of the kernels from an infinite kernel set, the margin is maximized subject to an infinite number of constraints with a compact index set and an additional (Riemann-Stieltjes) integral constraint due to the combinations. After a parametrization in the space of probability measures, we get a semi-infinite programming problem. We analyse regularity conditions (reduction ansatz) and discuss the type of density functions in the constraints and the bilevel optimization problem derived. Our proposed approach is implemented with the conceptual reduction method and tested on homogeneous and heterogeneous data;this yields a better accuracy than a single-kernel learning for the heterogeneous data. We analyse the structure of problems obtained and discuss structural frontiers, trade-offs and research challenges.

关键词： machine learning semi-infinite optimization infinite programming support vector machines continuous optimization data mining numerical methods

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Exact estimates of regularity modulus for infinite programming

Exact estimates of regularity modulus for infinite programmi...

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11th Workshop on Well-Posedness of Optimization Problems and Related Topics

作者： Sekiguchi, Yoshiyuki Tokyo Univ Marine Sci & Technol Fac Marine Technol Koto Ku Tokyo Japan

关键词： Modulus of metric regularity infinite programming

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