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作者：Noyan, Nilay; Merakli, Merve; Kucukyavuz, Simge
作者单位：Sabanci University; Northwestern University
摘要：In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features multivariate stochastic benchmarking constraints based on a vector-valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second-stage decisions. In particular, the aim is to ensure that the decision-based random outcome vector of interest is pref...
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作者：Beer, G.; Canovas, M. J.; Lopez, M. A.; Parra, J.
作者单位：California State University System; California State University Los Angeles; Universidad Miguel Hernandez de Elche; Universitat d'Alacant; Federation University Australia
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作者：Zhang, Haixiang; Milzarek, Andre; Wen, Zaiwen; Yin, Wotao
作者单位：University of California System; University of California Berkeley; The Chinese University of Hong Kong, Shenzhen; Shenzhen Research Institute of Big Data; Shenzhen Institute of Artificial Intelligence & Robotics for Society; Peking University; Peking University; University of California System; University of California Los Angeles
摘要：This paper considers the problem of solving a special quartic-quadratic optimization problem with a single sphere constraint, namely, finding a global and local minimizer of 1/2z*Az + beta/2 Sigma(n)(k=1) vertical bar z(k)vertical bar(4) such that parallel to z parallel to(2) = 1. This problem spans multiple domains including quantum mechanics and chemistry sciences and we investigate the geometric properties of this optimization problem. Fourth-order optimality conditions are derived for char...
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作者：Doikov, Nikita; Nesterov, Yurii
摘要：In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth component, having Lipschitz-continuous high-order derivative. The convergence both in function value and in the norm of minimal subgradient is established. Global complexity bounds for the Composite Tensor Method in convex and uniformly convex cases are also disc...
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作者：Bruggmann, Simon; Zenklusen, Rico
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Relaxation and rounding approaches became a standard and extremely versatile tool for constrained submodular function maximization. One of the most common rounding techniques in this context are contention resolution schemes. Such schemes round a fractional point by first rounding each coordinate independently, and then dropping some elements to reach a feasible set. Also the second step, where elements are dropped, is typically randomized. This leads to an additional source of randomization w...
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作者：Pashkovich, Kanstantsin
作者单位：University of Ottawa
摘要：In cooperative games, players have a possibility to form different coalitions. This leads to the questions about ways to motivate all players to collaborate, i.e. to motivate the players to form the so-called grand coalition. One of such ways is captured by the concept of nucleolus, which dates back to Babylonian Talmud. Weighted voting games form a class of cooperative games, that are often used to model decision making processes in parliaments. In this paper, we provide an algorithm for comp...
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作者：van Hoeve, Willem-Jan
作者单位：Carnegie Mellon University
摘要：We introduce an iterative framework for solving graph coloring problems using decision diagrams. The decision diagram compactly represents all possible color classes, some of which may contain edge conflicts. In each iteration, we use a constrained minimum network flow model to compute a lower bound and identify conflicts. Infeasible color classes associated with these conflicts are removed by refining the decision diagram. We prove that in the best case, our approach may use exponentially sma...
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作者：Lu, Cheng; Hochbaum, Dorit S.
作者单位：University of California System; University of California Berkeley
摘要：We study a 1-dimensional discrete signal denoising problem that consists of minimizing a sum of separable convex fidelity terms and convex regularization terms, the latter penalize the differences of adjacent signal values. This problem generalizes the total variation regularization problem. We provide here a unified approach to solve the problem for general convex fidelity and regularization functions that is based on the Karush-Kuhn-Tucker optimality conditions. This approach is shown here t...
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作者：Hoa, Le Tuan
作者单位：Vietnam Academy of Science & Technology (VAST)
摘要：The paper provides a connection between Commutative Algebra and Integer Programming and contains two parts. The first one is devoted to the asymptotic behavior of integer programs with a fixed cost linear functional and the constraint sets consisting of a finite system of linear equations or inequalities with integer coefficients depending linearly on n. An integer N-* is determined such that the optima of these integer programs are a quasi-linear function of n for all n >= N-*. Using results ...
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作者：Fan, Jingnan; Ruszczynski, Andrzej
作者单位：Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick
摘要：For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main feature is that they measure risk of processes that are functions of the history of a base process. We introduce a new concept of conditional stochastic time consistency and we derive the structure of process-based risk measures enjoying this property. We show that they can be equivalently represented by a collection of static law-invariant risk measures ...
