Partial Second-Order Subdifferentials in Variational Analysis and Optimization

  • Boris S. Mordukhovich
  • Nguyen Mau Nam
  • Nguyen Thi Yen Nhi
    • Categories Nonsmooth Optimization Tags , , , , , ,

    This paper presents a systematic study of partial second-order subdifferentials for extended-real-valued functions, which have already been applied to important issues of variational analysis and constrained optimization in finite-dimensional spaces. The main results concern developing extended calculus rules for these second-order constructions in both finite-dimensional and infinite-dimensional frameworks. We also provide new applications of partial … Read more

    Implementing cutting plane management and selection techniques

  • U. H. Suhl
  • Franz Wesselmann
    • Categories Cutting Plane Approaches Tags ,

    One main objective of research in the area of mixed-integer programming is developing cutting plane techniques to improve the solvability of mixed-integer programs (MIPs). Various cutting plane separators are typically available in MIP solvers. The large number of cutting planes generated by these separators, however, can pose a computational problem. Therefore, a sophisticated cut management … Read more

    Trajectories of Descent

  • Dmitriy Drusvyatskiy
  • Adrian Lewis
  • Alexander D. Ioffe
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    Steepest descent drives both theory and practice of nonsmooth optimization. We study slight relaxations of two influential notions of steepest descent curves — curves of maximal slope and solutions to evolution equations. In particular, we provide a simple proof showing that lower-semicontinuous functions that are locally Lipschitz continuous on their domains — functions playing a … Read more

    Common Mathematical Foundations of Expected Utility and Dual Utility Theories

  • Darinka Dentcheva
  • Andrzej Ruszczyński
    • Categories Stochastic Programming Tags , , , ,

    We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our analysis reveals the dual character of utility functions. We also derive new … Read more

    On metric regularity for weakly almost piecewise smooth functions and some applications in nonlinear semidefinite programming

  • Peter Fusek
    • Categories Semi-definite Programming Tags , , ,

    The one-to-one relation between the points fulfilling the KKT conditions of an optimization problem and the zeros of the corresponding Kojima function is well-known. In the present paper we study the interplay between metric regularity and strong regularity of this a priori nonsmooth function in the context of semidefinite programming. Having in mind the topological … Read more

    A Continuous Characterization of the Maximum-Edge Biclique Problem

  • Nicolas Gillis
  • François Glineur
    • Categories Data-Mining, Meta Heuristics Tags , , ,

    The problem of finding large complete subgraphs in bipartite graphs (that is, bicliques) is a well-known combinatorial optimization problem referred to as the maximum-edge biclique problem (MBP), and has many applications, e.g., in web community discovery, biological data analysis and text mining. In this paper, we present a new continuous characterization for MBP. Given a … Read more

    Constrained Bundle Methods for Upper Inexact Oracles with Application to Joint Chance Constrained Energy Problems

  • Claudia Sagastizábal
  • Wim van Ackooij
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , ,

    Joint chance constrained problems give rise to many algorithmic challenges. Even in the convex case, i.e., when an appropriate transformation of the probabilistic constraint is a convex function, its cutting-plane linearization is just an approximation, produced by an oracle providing subgradient and function values that can only be evaluated inexactly. As a result, the cutting-plane … Read more

    Reliable p-median facility location problem: two-stage robust models and algorithms

  • Yu An
  • Bo Zeng
  • Yu Zhang
  • Long Zhao
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    In this paper, we propose a set of two-stage robust optimization models to design reliable p-median facility location networks subject to disruptions. A customized column-and- constraint generation approach is implemented and shown to be more effective than Benders cutting plane method. Numerical experiments are performed on real data and management insights on system design are … Read more

    An Adaptive Augmented Lagrangian Method for Large-Scale Constrained Optimization

  • Frank E. Curtis
  • Daniel P. Robinson
  • Hao Jiang
    • Categories Nonlinear Optimization Tags , , , , ,

    We propose an augmented Lagrangian algorithm for solving large-scale constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improves the overall performance of the algorithm without sacrificing the strengths of the core augmented … Read more

    The Subset Sum Game

  • Andreas Darmann
  • Gaia Nicosia
  • Ulrich Pferschy
  • Joachim Schauer
    • Categories Combinatorial Optimization, Game Theory Tags , , ,

    In this work we address a game theoretic variant of the Subset Sum problem, in which two decision makers (agents/players) compete for the usage of a common resource represented by a knapsack capacity. Each agent owns a set of integer weighted items and wants to maximize the total weight of its own items included in … Read more