Month: January 2009

Optimality conditions for several type of efficient solutions of set-valued optimization problems

  • Xuan Duc Ha Truong
    • Categories Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , , , , ,

    A simple unified framework is presented for the study of strong efficient solutions, weak efficient solutions, positive proper efficient solutions, Henig global proper efficient solutions, Henig proper efficient solutions, super efficient solutions, Benson proper efficient solutions, Hartley proper efficient solutions, Hurwicz proper efficient solutions and Borwein proper efficient solutions of set-valued optimization problem with/or without … Read more

    Identifying Activity

  • Adrian Lewis
  • Stephen Wright
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    Identification of active constraints in constrained optimization is of interest from both practical and theoretical viewpoints, as it holds the promise of reducing an inequality-constrained problem to an equality-constrained problem, in a neighborhood of a solution. We study this issue in the more general setting of composite nonsmooth minimization, in which the objective is a … Read more

    Asset-Liability Management Modelling with Risk Control by Stochastic Dominance

  • Jacek Gondzio
  • Andreas Grothey
  • Xi Yang
    • Categories Finance and Economics, Parallel Algorithms, Stochastic Programming Tags , , ,

    An Asset-Liability Management model with a novel strategy for controlling risk of underfunding is presented in this paper. The basic model involves multiperiod decisions (portfolio rebalancing) and deals with the usual uncertainty of investment returns and future liabilities. Therefore it is well-suited to a stochastic programming approach. A stochastic dominance concept is applied to measure … Read more

    Fejer processes with diminishing disturbances and decomposition of constrained nondifferentiable optimization problems

  • Evgeni Alekseevich Nurminski
    • Categories Convex and Nonsmooth Optimization Tags ,

    Iterative processes based on Fejer mappings with diminishing problem-specific shifts in the arguments are considered. Such structure allows fine-tuning of Fejer processes by directing them toward selected subsets of attracting sets. Use of various Fejer operators provides ample opportunities for decomposition and parallel computations. Subgradient projection algorithms with sequential and simultaneous projections on segmented constraints … Read more

    Robust Portfolio Optimization with Derivative Insurance Guarantees

  • Daniel Kuhn
  • Berc Rustem
  • Steve Zymler
    • Categories Finance and Economics, Robust Optimization Tags , , ,

    Robust portfolio optimization finds the worst-case portfolio return given that the asset returns are realized within a prescribed uncertainty set. If the uncertainty set is not too large, the resulting portfolio performs well under normal market conditions. However, its performance may substantially degrade in the presence of market crashes, that is, if the asset returns … Read more

    Exploiting Sparsity in Linear and Nonlinear Matrix Inequalities via Positive Semidefinite Matrix Completion

  • Sunyoung Kim
  • Masakazu Kojima
  • Martin Mevissen
  • Makoto Yamashita
    • Categories Semi-definite Programming Tags , , ,

    A basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities. The sparsity, characterized with a chordal graph structure, can be detected in the variable matrix or in a linear or nonlinear matrix-inequality constraint of the problem. We classify the sparsity in two … Read more

    OSPF Routing with Optimal Oblivious Performance Ratio Under Polyhedral Demand Uncertainty

  • Aysegul Altin
  • Pietro Belotti
  • Mustafa C. Pinar
    • Categories Network Optimization, Robust Optimization, Telecommunications Tags , , , , , ,

    We study the best OSPF style routing problem in telecommunication networks, where weight management is employed to get a routing configuration with the minimum oblivious ratio. We consider polyhedral demand uncertainty: the set of traffic matrices is a polyhedron defined by a set of linear constraints, and the performance of each routing is assessed on … Read more

    Solving multi-objective network flow problems with an interior point method

  • José Rui Figureira
  • Margarida Fonseca
  • Mauricio G.C. Resende
    • Categories Linear Programming, Multi-Criteria Optimization, Network Optimization Tags , , ,

    In this paper we present a primal-dual interior-point algorithm to solve a class of multi-objective network flow problems. More precisely, our algorithm is an extension of the single-objective primal-dual infeasible and inexact interior point method for multi-objective linear network flow problems. A comparison with standard interior point methods is provided and experimental results on bi-objective … Read more

    Theta Bodies for Polynomial Ideals

  • João Gouveia
  • Pablo A. Parrilo
  • Rekha R. Thomas
    • Categories Approximation Algorithms, Semi-definite Programming Tags , ,

    Inspired by a question of Lov\’asz, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta bodies of the ideal. For the stable set problem in a graph, the first theta body in this hierarchy is exactly Lov{\’a}sz’s theta body of the graph. … Read more

    Hybrid MPI/OpenMP parallel support vector machine training

  • Jacek Gondzio
  • Kristian Woodsend
    • Categories Data-Mining, Parallel Algorithms, Quadratic Programming Tags , , ,

    Support Vector Machines are a powerful machine learning technology, but the training process involves a dense quadratic optimization problem and is computationally challenging. A parallel implementation of Support Vector Machine training has been developed, using a combination of MPI and OpenMP. Using an interior point method for the optimization and a reformulation that avoids the … Read more