On nonsmooth and discontinuous problems of stochastic systems optimization |
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| Institution: | 1. Department of Information Technology, Hunan Women’s University, Changsha, Hunan 410002, China;2. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China;3. College of Science, National University of Defense Technology, Changsha, Hunan 410073, China;1. College of Arts and Sciences, Shanghai Polytechnic University, Shanghai 201209, China;2. School of Cyberspace Security, Northwestern Polytechnical University, Xi’an 710072, China;3. Department of Mathematics, University of Houston, Houston 77004, Texas, USA |
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| Abstract: | A class of stochastic optimization problems is analyzed that cannot be solved by deterministic and standard stochastic approximation methods. We consider risk-control problems, optimization of stochastic networks and discrete event systems, screening irreversible changes, and pollution control. The results of Ermoliev et al. are extended to the case of stochastic systems and general constraints. It is shown that the concept of stochastic mollifier gradient leads to easily implementable computational procedures for systems with Lipschitz and discontinuous objective functions. New optimality conditions are formulated for designing stochastic search procedures for constrained optimization of discontinuous systems. |
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