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作者：Xie, Weijun
作者单位：Virginia Polytechnic Institute & State University
摘要：This paper studies a distributionally robust chance constrained program (DRCCP) with Wasserstein ambiguity set, where the uncertain constraints should be satisfied with a probability at least a given threshold for all the probability distributions of the uncertain parameters within a chosen Wasserstein distance from an empirical distribution. In this work, we investigate equivalent reformulations and approximations of such problems. We first show that a DRCCP can be reformulated as a condition...
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作者：Flores-Bazan, F.; Garcia, Y.; Hadjisavvas, N.
作者单位：Universidad de Concepcion; Universidad del Pacifico Peru; University of Aegean
摘要：It is well-known that the sum of two quasiconvex functions is not quasiconvex in general, and the same occurs with the minimum. Although apparently these two statements (for the sum or minimum) have nothing in common, they are related, as we show in this paper. To develop our study, the notion of quasiconvex family is introduced, and we establish various characterizations of such a concept: one of them being the quasiconvexity of the pointwise infimum of arbitrary translations of quasiconvex f...
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作者：Xu, Yangyang
作者单位：Rensselaer Polytechnic Institute
摘要：Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence and local convergence speed of ALM have been extensively studied. However, the global convergence rate of the inexact ALMis still open for problems with nonlinear inequality constraints. In this paper, we work on general convex programs with both equality and ...
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作者：Dutta, Joydeep; Enrique Martinez-Legaz, Juan
作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Kanpur; Autonomous University of Barcelona
摘要：The main goal in this paper is to devise an approach to explicitly calculate the constant in the Hoffman's error bound for (notnecessarily convex) inequality systems defining convex sets. We give a constructive proof of the Hoffman's error bound and show that we can use our method to calculate the constant at least in simple cases.
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作者：Bah, Bubacarr; Kurtz, Jannis; Schaudt, Oliver
作者单位：Stellenbosch University; RWTH Aachen University
摘要：In this article we study the problem of signal recovery for group models. More precisely for a given set of groups, each containing a small subset of indices, and for given linear sketches of the true signal vector which is known to be group-sparse in the sense that its support is contained in the union of a small number of these groups, we study algorithms which successfully recover the true signal just by the knowledge of its linear sketches. We derive model projection complexity results and...
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作者：Chubanov, Sergei
摘要：In this paper we present a scaling algorithm for minimizing arbitrary functions over vertices of polytopes in an oracle model of computation which includes an augmentation oracle. For the binary case, when the vertices are 0-1 vectors, we show that the oracle time is polynomial. Also, this algorithm allows us to generalize some concepts of combinatorial optimization concerning performance bounds of greedy algorithms and leads to new bounds for the complexity of the simplex method.
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作者：Martinez-Legaz, Juan Enrique; Pintea, Cornel
作者单位：Autonomous University of Barcelona; Babes Bolyai University from Cluj
摘要：We characterize the closed convex subsets of R-n which have open or closed Gauss ranges. Some special attention is paid to epigraphs of lower semicontinuous convex functions.
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作者：Adly, S.; Nacry, F.; Thibault, L.
作者单位：Universite de Limoges; Universite Perpignan Via Domitia; Universite de Montpellier
摘要：In this paper, we present diverse new metric properties that prox-regular sets shared with convex ones. At the heart of our work lie the Legendre-Fenchel transform and complements of balls. First, we show that a connected prox-regular set is completely determined by the Legendre-Fenchel transform of a suitable perturbation of its indicator function. Then, we prove that such a function is also the right tool to extend, to the context of prox-regular sets, the famous connection between the dista...
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作者：Benedek, Marton; Fliege, Jorg; Tri-Dung Nguyen
作者单位：HUN-REN; HUN-REN Centre for Economic & Regional Studies; Institute of Economics - HAS; Hungarian Academy of Sciences; Corvinus University Budapest; Budapest University of Technology & Economics; University of Southampton; University of Southampton; University of Southampton
摘要：The nucleolus offers a desirable payoff-sharing solution in cooperative games, thanks to its attractive properties-it always exists and lies in the core (if the core is nonempty), and it is unique. The nucleolus is considered as the most `stable' solution in the sense that it lexicographically minimizes the dissatisfactions among all coalitions. Although computing the nucleolus is very challenging, the Kohlberg criterion offers a powerful method for verifying whether a solution is the nucleolu...
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作者：Fuellner, Christian; Kirst, Peter; Stein, Oliver
作者单位：Helmholtz Association; Karlsruhe Institute of Technology
摘要：We address the problem of determining convergent upper bounds in continuous non-convex global minimization of box-constrained problems with equality constraints. These upper bounds are important for the termination of spatial branch-and-bound algorithms. Our method is based on the theorem of Miranda which helps to ensure the existence of feasible points in certain boxes. Then, the computation of upper bounds at the objective function over those boxes yields an upper bound for the globally mini...
