3期

最新文章

• A Moment-Sum-of-Squares Hierarchy for Robust Polynomial Matrix Inequality Optimization with Sum-of-Squares Convexity AI翻译
  作者：Guo, Feng; Wang, Jie
  作者单位：Dalian University of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
  摘要：We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is also defined by a PMI. These can be viewed as matrix generalizations of semi-infinite polynomial programs because they involve actually infinitely many PMI constraints in general. Under certain sum-of-squares (SOS)-convexity assumptions, we construct a hierarchy of increasingly tight moment-SOS relaxations for solving such problems. Most of the ni...
• Optimality Conditions in Control Problems with Random State Constraints in Probabilistic or Almost Sure Form AI翻译
  作者：Geiersbach, Caroline; Henrion, Rene
  作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
  摘要：In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. Although the latter can be understood as the limiting case of the former, the derivation of optimality conditions requires substantially different approaches. We apply them to a linear elliptic partial differential equation with random inputs. In the probabilistic case, we rely on the spherical-radial decomposition of Gaussian ran...
• An Augmented Lagrangian Approach to Conically Constrained Nonmonotone Variational Inequality Problems AI翻译
  作者：Zhao, Lei; Zhu, Daoli; Zhang, Shuzhong
  作者单位：Shanghai Jiao Tong University; Shanghai Jiao Tong University; Shanghai Jiao Tong University; The Chinese University of Hong Kong, Shenzhen; Shenzhen Research Institute of Big Data; University of Minnesota System; University of Minnesota Twin Cities
  摘要：In this paper we consider a nonmonotone (mixed) variational inequality (VI) model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like primal-dual saddle point system for the VI model in question, we introduce an augmented Lagrangian primal-dual method, called ALAVI (Augmented Lagrangian Approach to Variational Inequality) in the paper, for solving a general constrained VI model. Under an assumption, called the primal-dual variational coherence c...
• Langevin Dynamics Based Algorithm e-THεO POULA for Stochastic Optimization Problems with Discontinuous Stochastic Gradient AI翻译
  作者：Lim, Dong-Young; Neufeld, Ariel; Sabanis, Sotirios; Zhang, Ying
  作者单位：Ulsan National Institute of Science & Technology (UNIST); Nanyang Technological University; University of Edinburgh; Alan Turing Institute; National Technical University of Athens; Hong Kong University of Science & Technology (Guangzhou)
  摘要：We introduce a new Langevin dynamics based algorithm, called the extended tamed hybrid epsilon-order polygonal unadjusted Langevin algorithm (e-TH epsilon O POULA), to solve optimization problems with discontinuous stochastic gradients, which naturally appear in real-world applications such as quantile estimation, vector quantization, conditional value at risk (CVaR) minimization, and regularized optimization problems involving rectified linear unit (ReLU) neural networks. We demonstrate both ...
• Erratum to: Linear Convergence of Dual Coordinate Descent on Nonpolyhedral Convex Problems AI翻译
  作者：Necoara, Ion; Fercoq, Olivier
  作者单位：National University of Science & Technology POLITEHNICA Bucharest; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
  摘要：Our proof of linear convergence for Dykstra's algorithm was erroneous, and in fact, there even exists a counterexample showing that the result is false.
• Fair Shares: Feasibility, Domination, and Incentives AI翻译
  作者：Babaioff, Moshe; Feige, Uriel
  作者单位：Hebrew University of Jerusalem; Weizmann Institute of Science
  摘要：We consider fair allocation of indivisible goods to n equally entitled agents. Every agent i has a valuation function vi from some given class of valuation functions. A share s is a function that maps (vi, n) to a nonnegative value. A share is feasible if for every allocation instance, there is an allocation that gives every agent i a bundle that is acceptable with respect to vi, one of value at least her share value s(vi, n). We introduce the following concepts. A share is self-maximizing if ...
• Optimal Ratcheting of Dividends with Capital Injection AI翻译
  作者：Wang, Wenyuan; Xu, Ran; Van, Kaixin
  作者单位：Fujian Normal University; Fujian Normal University; Fujian Normal University; Fujian Normal University; Fujian Normal University; Xiamen University; Xi'an Jiaotong-Liverpool University
  摘要：In this paper, we investigate the optimal dividend problem with capital injection and ratcheting constraint with nondecreasing dividend payout rate. Capital injections are introduced in order to eliminate the possibility of bankruptcy. Under the Cramer-Lundberg risk model, the problem is formulated as a two-dimensional stochastic control problem. By applying the viscosity theory, we show that the value function is the unique viscosity solution to the associated Hamilton-Jacobi-Bellman equation...
• Parabolic Regularity of Spectral Functions AI翻译
  作者：Mohammadi, Ashkan; Sarabi, Ebrahim
  作者单位：Georgetown University; University System of Ohio; Miami University
  摘要：This paper is devoted to the study of the second-order variational analysis of spectral functions. It is well-known that spectral functions can be expressed as a composite function of symmetric functions and eigenvalue functions. We establish several secondorder properties of spectral functions when their associated symmetric functions enjoy these properties. Our main attention is given to characterize parabolic regularity for this class of functions. It was observed recently that parabolic re...
• Exploration Noise for Learning Linear-Quadratic Mean Field Games AI翻译
  作者：Delarue, Francois; Vasileiadis, Athanasios
  作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
  摘要：The goal of this paper is to demonstrate that common noise may serve as an exploration noise for learning the solution of a mean field game. This concept is here exemplified through a toy linear-quadratic model, for which a suitable form of common noise has already been proven to restore existence and uniqueness. We here go one step further and prove that the same form of common noise may force the convergence of the learning algorithm called fictitious play, and this without any further poten...
• Information Design and Sharing in Supply Chains AI翻译
  作者：Caldentey, Rene; Giloni, Avi; Hurvich, Clifford; Zhang, Yichen
  作者单位：University of Chicago; Yeshiva University; New York University; Purdue University System; Purdue University
  摘要：We study the interplay between inventory replenishment policies and information sharing in the context of a two-tier supply chain with a single supplier and a single retailer serving an independent and identically distributed Gaussian market demand. We investigate how the retailer's inventory policy impacts the supply chain's cumulative expected long-term average inventory costs C in two extreme information-sharing cases: (a) full information sharing and (b) no information sharing. To find the...