1-2期

最新文章

• Nonanticipative duality, relaxations, and formulations for chance-constrained stochastic programs AI翻译
  作者：Ahmed, Shabbir; Luedtke, James; Song, Yongjia; Xie, Weijun
  作者单位：University System of Georgia; Georgia Institute of Technology; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; Virginia Commonwealth University
  摘要：We propose two new Lagrangian dual problems for chance-constrained stochastic programs based on relaxing nonanticipativity constraints. We compare the strength of the proposed dual bounds and demonstrate that they are superior to the bound obtained from the continuous relaxation of a standard mixed-integer programming (MIP) formulation. For a given dual solution, the associated Lagrangian relaxation bounds can be calculated by solving a set of single scenario subproblems and then solving a sin...
• Continuous location under the effect of 'refraction' AI翻译
  作者：Blanco, Victor; Puerto, Justo; Ponce, Diego
  作者单位：University of Granada; University of Sevilla; University of Sevilla
  摘要：In this paper we address the problem of locating a new facility on a d-dimensional space when the distance measure (- or polyhedral-norms) is different at each one of the sides of a given hyperplane . We relate this problem with the physical phenomenon of refraction, and extend it to any finite dimensional space and different distances at each one of the sides of any hyperplane. An application to this problem is the location of a facility within or outside an urban area where different distanc...
• On the time transformation of mixed integer optimal control problems using a consistent fixed integer control function AI翻译
  作者：Ringkamp, Maik; Ober-Blobaum, Sina; Leyendecker, Sigrid
  作者单位：University of Erlangen Nuremberg; University of Oxford
  摘要：Nonlinear control systems with instantly changing dynamical behavior can be modeled by introducing an additional control function that is integer valued in contrast to a control function that is allowed to have continuous values. The discretization of a mixed integer optimal control problem (MIOCP) leads to a non differentiable optimization problem and the non differentiability is caused by the integer values. The paper is about a time transformation method that is used to transform a MIOCP wi...
• A fresh CP look at mixed-binary QPs: new formulations and relaxations AI翻译
  作者：Bomze, Immanuel M.; Cheng, Jianqiang; Dickinson, Peter J. C.; Lisser, Abdel
  作者单位：University of Vienna; University of Arizona; University of Twente; Universite Paris Saclay
  摘要：Triggered by Burer's seminal characterization from 2009, many copositive reformulations of mixed-binary QPs have been discussed by now. Most of them can be used as proper relaxations, if the intractable co(mpletely)positive cones are replaced by tractable approximations. While the widely used approximation hierarchies have the disadvantage to use positive-semidefinite (psd) matrices of orders which rapidly increase with the level of approximation, alternatives focus on the problem of keeping p...
• Finding a low-rank basis in a matrix subspace AI翻译
  作者：Nakatsukasa, Yuji; Soma, Tasuku; Uschmajew, Andre
  作者单位：University of Oxford; University of Tokyo; University of Bonn; University of Bonn
  摘要：For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained by the tensor CP decomposition. For the higher rank case, the situation is not as straightforward. In this work we present an algorithm based on a greedy process applicable to higher rank problems. Our algorithm first estimates the minimum rank by applying s...
• Quadratic reformulations of nonlinear binary optimization problems AI翻译
  作者：Anthony, Martin; Boros, Endre; Crama, Yves; Gruber, Aritanan
  作者单位：University of London; London School Economics & Political Science; Rutgers University System; Rutgers University New Brunswick; Rutgers University System; Rutgers University New Brunswick; University of Liege; Universidade de Sao Paulo
  摘要：Very large nonlinear unconstrained binary optimization problems arise in a broad array of applications. Several exact or heuristic techniques have proved quite successful for solving many of these problems when the objective function is a quadratic polynomial. However, no similarly efficient methods are available for the higher degree case. Since high degree objectives are becoming increasingly important in certain application areas, such as computer vision, various techniques have been recent...
• An efficient inexact symmetric Gauss-Seidel based majorized ADMM for high-dimensional convex composite conic programming AI翻译
  作者：Chen, Liang; Sun, Defeng; Toh, Kim-Chuan
  作者单位：Hunan University; National University of Singapore; National University of Singapore
  摘要：In this paper, we propose an inexact multi-block ADMM-type first-order method for solving a class of high-dimensional convex composite conic optimization problems to moderate accuracy. The design of this method combines an inexact 2-block majorized semi-proximal ADMM and the recent advances in the inexact symmetric Gauss-Seidel (sGS) technique for solving a multi-block convex composite quadratic programming whose objective contains a nonsmooth term involving only the first block-variable. One ...
• The Ancestral Benders' cutting plane algorithm with multi-term disjunctions for mixed-integer recourse decisions in stochastic programming AI翻译
  作者：Qi, Yunwei; Sen, Suvrajeet
  作者单位：University System of Ohio; Ohio State University; University of Southern California
  摘要：This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first-stage approximation is solved by a branch-and-bound algorithm with its nodes inheriting Benders' cuts that are valid for their ancestor nodes. In addition, we develop two closely related convexification schemes which use multi-term disjunctive cuts to obtain approximations of the second-stage mixe...
• Stochastic compositional gradient descent: algorithms for minimizing compositions of expected-value functions AI翻译
  作者：Wang, Mengdi; Fang, Ethan X.; Liu, Han
  作者单位：Princeton University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
  摘要：Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value functions, i.e., the problem In order to solve this stochastic composition problem, we propose a class of stochastic compositional gradient descent (SCGD) algorithms that can be viewed as stochastic versions of quasi-gradient method. SCGD update the solutio...
• Variational analysis of the Crouzeix ratio AI翻译
  作者：Greenbaum, Anne; Lewis, Adrian S.; Overton, Michael L.
  作者单位：University of Washington; University of Washington Seattle; Cornell University; New York University
  摘要：Let W(A) denote the field of values (numerical range) of a matrix A. For any polynomial p and matrix A, define the Crouzeix ratio to have numerator and denominator . Crouzeix's 2004 conjecture postulates that the globally minimal value of the Crouzeix ratio is 1 / 2, over all polynomials p of any degree and matrices A of any order. We derive the subdifferential of this ratio at pairs (p, A) for which the largest singular value of p(A) is simple. In particular, we show that at certain candidate...