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作者：Saxena, Anureet; Goyal, Vineet; Lejeune, Miguel A.
作者单位：Drexel University; Carnegie Mellon University
摘要：In this paper, we address the following probabilistic version (PSC) of the set covering problem: min{cx vertical bar P(Ax >= xi) >= p, x is an element of {0, 1}(N)} where A is a 0-1 matrix, xi is a random 0-1 vector and p is an element of (0, 1] is the threshold probability level. We introduce the concepts of p-inefficiency and polarity cuts. While the former is aimed at deriving an equivalent MIP reformulation of (PSC), the latter is used as a strengthening device to obtain a stronger formula...
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作者：Gould, N. I. M.; Toint, Ph. L.
作者单位：University of Namur; University of Oxford
摘要：A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, and allows inexact SQP steps that do not lie exactly in the nullspace of the local Jacobian. Preliminary numerical experiments on CUTEr problems indicate...
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作者：Gutierrez, C.; Jimenez, B.; Novo, V.
作者单位：Universidad Nacional de Educacion a Distancia (UNED); Universidad de Valladolid
摘要：We study a multiobjective optimization program with a feasible set defined by equality constraints and a generalized inequality constraint. We suppose that the functions involved are Fr,chet differentiable and their Fr,chet derivatives are continuous or stable at the point considered. We provide necessary second order optimality conditions and also sufficient conditions via a Fritz John type Lagrange multiplier rule and a set-valued second order directional derivative, in such a way that our s...
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作者：Anitescu, Mihai; Park, Sanghyun
作者单位：United States Department of Energy (DOE); Argonne National Laboratory
摘要：This work addresses the computation of free-energy differences between protein conformations by using morphing (i.e., transformation) of a source conformation into a target conformation. To enhance the morphing procedure, we employ permutations of atoms: we seek to find the permutation sigma that minimizes the mean-square distance traveled by the atoms. Instead of performing this combinatorial search in the space of permutations, we show that the best permutation can be found by solving a line...
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作者：Helton, J. William; Nie, Jiawang
作者单位：University of California System; University of California San Diego
摘要：Let S = {x is an element of R-n : g(1)(x) >= 0, ..., g(m)(x) >= 0} be a semialgebraic set defined by multivariate polynomials g(i) (x). Assume S is convex, compact and has nonempty interior. Let S-i = {x is an element of R-n : g(i)(x) >= 0}, and partial derivative S (resp. partial derivative S-i ) be the boundary of S (resp. S-i ). This paper, as does the subject of semidefinite programming (SDP), concerns linear matrix inequalities (LMIs). The set S is said to have an LMI representation if it...
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作者：Crouzeix, Jean-Pierre; Eberhard, Andrew; Ralph, Daniel
作者单位：Universite Clermont Auvergne (UCA); Royal Melbourne Institute of Technology (RMIT); University of Cambridge
摘要：Generalised convexity is revisited from a geometric point of view. A substitute to the subdifferential is proposed. Then generalised monotonicity is considered. A representation of generalised monotone maps allows us to obtain a symmetry between maps and their inverses. Finally, maximality of generalised monotone maps is analysed.
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作者：Atamtuerk, Alper; Narayanan, Vishnu
作者单位：University of California System; University of California Berkeley
摘要：A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures of second-order conic sets. These cuts can be readily incorporated in branch-and-bound algorithms tha...
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作者：Dinh, N.; Mordukhovich, B.; Nghia, T. T. A.
作者单位：Vietnam National University Ho Chi Minh City (VNUHCM) System; Wayne State University
摘要：The paper concerns the study of new classes of parametric optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain, among other constraints, infinitely many inequality constraints. These problems reduce to semi-infinite programs in the case of finite-dimensional spaces of decision variables. We focus on DC infinite programs with objectives given as the difference of convex functions subject to convex...
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作者：Han, Lanshan; Pang, Jong-Shi
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：The Zeno phenomenon of a switched dynamical system refers to the infinite number of mode switches in finite time. The absence of this phenomenon is crucial to the numerical simulation of such a system by time-stepping methods and to the understanding of the behavior of the system trajectory. Extending a previous result for a strongly regular differential variational inequality, this paper establishes that a certain class of non-strongly regular differential variational inequalities is devoid o...
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作者：Richard, Jean-Philippe P.; Tawarmalani, Mohit
作者单位：Purdue University System; Purdue University; Purdue University System; Purdue University
摘要：In this paper, we introduce the first generic lifting techniques for deriving strong globally valid cuts for nonlinear programs. The theory is geometric and provides insights into lifting-based cut generation procedures, yielding short proofs of earlier results in mixed-integer programming. Using convex extensions, we obtain conditions that allow for sequence-independent lifting in nonlinear settings, paving a way for efficient cut-generation procedures for nonlinear programs. This sequence-in...
