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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：Kaparis, Konstantinos; Letchford, Adam N.
作者单位：Lancaster University; University of Southampton
摘要：Valid inequalities for 0-1 knapsack polytopes often prove useful when tackling hard 0-1 Linear Programming problems. To generate such inequalities, one needs separation algorithms for them, i.e., routines for detecting when they are violated. We present new exact and heuristic separation algorithms for several classes of inequalities, namely lifted cover, extended cover, weight and lifted pack inequalities. Moreover, we show how to improve a recent separation algorithm for the 0-1 knapsack pol...
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作者：Yuan, Ya-xiang
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：This short note gives the sharp bound for the Q-linear convergence rate of the iterates generated by the steepest descent method with exact line searches when the objective function is strictly convex quadratic.
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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：Elhallaoui, Issmail; Metrane, Abdelmoutalib; Soumis, Francois; Desaulniers, Guy
作者单位：Universite de Montreal; Polytechnique Montreal; Universite de Montreal
摘要：Dynamic constraint aggregation is an iterative method that was recently introduced to speed up the linear relaxation solution process of set partitioning type problems. This speed up is mostly due to the use, at each iteration, of an aggregated problem defined by aggregating disjoint subsets of constraints from the set partitioning model. This aggregation is updated when needed to ensure the exactness of the overall approach. In this paper, we propose a new version of this method, called the m...
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作者：Rendl, Franz; Rinaldi, Giovanni; Wiegele, Angelika
作者单位：University of Klagenfurt; Consiglio Nazionale delle Ricerche (CNR); Istituto di Analisi dei Sistemi ed Informatica Antonio Ruberti (IASI-CNR)
摘要：We present a method for finding exact solutions of Max-Cut, the problem of finding a cut of maximum weight in a weighted graph. We use a Branch-and-Bound setting that applies a dynamic version of the bundle method as bounding procedure. This approach uses Lagrangian duality to obtain a nearly optimal solution of the basic semidefinite Max-Cut relaxation, strengthened by triangle inequalities. The expensive part of our bounding procedure is solving the basic semidefinite relaxation of the Max-C...
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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...
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作者：Pang, Jong-Shi
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：Celebrating the sixtieth anniversary since the zeroth International Symposium on Mathematical Programming was held in 1949, this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field. These are: competition, dynamics, and hierarchy. The discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive, equilibrium, and nonl...
