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作者：Grechuk, Bogdan; Zabarankin, Michael
作者单位：University of Leicester; Stevens Institute of Technology
摘要：In a regression with independent and identically distributed normal residuals, the log-likelihood function yields an empirical form of the L-2-norm, whereas the normal distribution can be obtained as a solution of differential entropy maximization subject to a constraint on the L-2-norm of a random variable. The L-1-norm and the double exponential (Laplace) distribution are related in a similar way. These are examples of an inter-regenerative relationship. In fact, L-2-norm and L-1-norm are ju...
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作者：Shapiro, Alexander
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：In this paper we consider covariance structural models with which we associate semidefinite programming problems. We discuss statistical properties of estimates of the respective optimal value and optimal solutions when the 'true' covariance matrix is estimated by its sample counterpart. The analysis is based on perturbation theory of semidefinite programming. As an example we consider asymptotics of the so-called minimum trace factor analysis. We also discuss the minimum rank matrix completio...
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作者：Range, Troels Martin; Osterdal, Lars Peter
作者单位：University of Southern Denmark; University of Southern Denmark; Norwegian University of Science & Technology (NTNU); Copenhagen Business School
摘要：How to determine whether one distribution first-order dominates another is a fundamental problem that has many applications in economics, finance, probability theory, and statistics. Nevertheless, little is known about how to efficiently check first-order dominance for finite multivariate distributions. Utilizing that this problem can be formulated as a transportation problem with a special structure, we provide a stronger characterization of multivariate first-order dominance and develop a li...
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作者：Schmidt, Martin; Sirvent, Mathias; Wollner, Winnifried
作者单位：University of Erlangen Nuremberg; University of Erlangen Nuremberg; Technical University of Darmstadt
摘要：Many mixed-integer optimization problems are constrained by nonlinear functions that do not possess desirable analytical properties like convexity or factorability or cannot even be evaluated exactly. This is, e.g., the case for many problems constrained by differential equations or for models that rely on black-box simulation runs. For these problem classes, we present, analyze, and test algorithms that solve mixed-integer problems with Lipschitz continuous nonlinearities. Our theoretical res...
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作者：Hojny, Christopher; Pfetsch, Marc E.
作者单位：Technical University of Darmstadt
摘要：This paper investigates a polyhedral approach to handle symmetries in mixed-binary programs. We study symretopes, i.e., the convex hulls of all binary vectors that are lexicographically maximal in their orbit with respect to the symmetry group. These polytopes turn out to be quite complex. For practical use, we therefore develop an integer programming formulation with ternary coefficients, based on knapsack polytopes arising from a single lexicographic order enforcing inequality. We show that ...
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作者：Chen, Caihua; Li, Min; Liu, Xin; Ye, Yinyu
作者单位：Nanjing University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Stanford University
摘要：In this paper, we establish the convergence of the proximal alternating direction method of multipliers (ADMM) and block coordinate descent (BCD) method for nonseparable minimization models with quadratic coupling terms. The novel convergence results presented in this paper answer several open questions that have been the subject of considerable discussion. We firstly extend the 2-block proximal ADMM to linearly constrained convex optimization with a coupled quadratic objective function, an ar...
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作者：Cui, Ying; Sun, Defeng; Toh, Kim-Chuan
作者单位：University of Southern California; Hong Kong Polytechnic University; National University of Singapore
摘要：Due to the possible lack of primal-dual-type error bounds, it was not clear whether the Karush-Kuhn-Tucker (KKT) residuals of the sequence generated by the augmented Lagrangian method (ALM) for solving convex composite conic programming (CCCP) problems converge superlinearly. In this paper, we resolve this issue by establishing the R-superlinear convergence of the KKT residuals generated by the ALM under only a mild quadratic growth condition on the dual of CCCP, with easy-to-implement stoppin...
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作者：Guo, Shaoyan; Xu, Huifu
作者单位：Dalian University of Technology; University of Southampton
摘要：Utility-based shortfall risk measures (SR) have received increasing attention over the past few years for their potential to quantify the risk of large tail losses more effectively than conditional value at risk. In this paper, we consider a distributionally robust version of the shortfall risk measure (DRSR) where the true probability distribution is unknown and the worst distribution from an ambiguity set of distributions is used to calculate the SR. We start by showing that the DRSR is a co...
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作者：Bellavia, Stefania; Gondzio, Jacek; Porcelli, Margherita
作者单位：University of Florence; University of Edinburgh; Research & Academic Computer Network (NASK)
摘要：A dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S. It relies on inexact Newton steps in dual space which are computed by the conjugate gradient method applied to the Schur complement of the reduced KKT system. The method may take advantage of low-rank representations of matrices Ai to perform implicit matrix-...
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作者：Chen, Xiaojun; Sun, Hailin; Xu, Huifu
作者单位：Hong Kong Polytechnic University; Nanjing University of Science & Technology; University of Southampton
摘要：In this paper, we propose a discretization scheme for the two-stage stochastic linear complementarity problem (LCP) where the underlying random data are continuously distributed. Under some moderate conditions, we derive qualitative and quantitative convergence for the solutions obtained from solving the discretized two-stage stochastic LCP (SLCP). We explain how the discretized two-stage SLCP may be solved by the well-known progressive hedging method (PHM). Moreover, we extend the discussion ...
