Month: August 2001

SDPT3 – a MATLAB software package for semidefinite-quadratic-linear programming, version 3.0

  • Michael J. Todd
  • Kim-Chuan Toh
  • Reha H. Tütüncü
    • Categories Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , , ,

    This software package is a MATLAB implementation of infeasible path-following algorithms for solving conic programming problems whose constraint cone is a product of semidefinite cones, second-order cones, and/or nonnegative orthants. It employs a predictor-corrector primal-dual path-following method, with either the HKM or the NT search direction. The basic code is written in Matlab, but key … Read more

    Global and Local Convergence of Line Search Filter Methods for Nonlinear Programming

  • Lorenz T. Biegler
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization Tags , , , , , , , , , ,

    Line search methods for nonlinear programming using Fletcher and Leyffer’s filter method, which replaces the traditional merit function, are proposed and their global and local convergence properties are analyzed. Previous theoretical work on filter methods has considered trust region algorithms and only the question of global convergence. The presented framework is applied to barrier interior … Read more

    Semi-infinite linear programming approaches to semidefinite programming problems

  • Kartik Krishnan
  • John E. Mitchell
    • Categories Convex and Nonsmooth Optimization, Infinite Dimensional Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    Interior point methods, the traditional methods for the $SDP$, are fairly limited in the sizes of problems they can handle. This paper deals with an $LP$ approach to overcome some of these shortcomings. We begin with a semi-infinite linear programming formulation of the $SDP$ and discuss the issue of its discretization in some detail. We … Read more

    A Remarkable Property of the Dynamic Optimization Extremals

  • Delfim F. M. Torres
    • Categories Systems governed by Differential Equations Optimization Tags , , ,

    A dynamic optimization continuous problem poses the question of what is the optimal magnitude of a choice variable, at each point of time, in a given interval. To tackle such problems, three major approaches are available: dynamic programming; the calculus of variations; and the powerful optimal control approach. At the core of optimal control theory … Read more

    On the Primal-Dual Geometry of Level Sets in Linear and Conic Optimization

  • Robert M. Freund
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    For a conic optimization problem: minimize cx subject to Ax=b, x \in C, we present a geometric relationship between the maximum norms of the level sets of the primal and the inscribed sizes of the level sets of the dual (or the other way around). Citation MIT Operations Research Center Working Paper Article Download View … Read more

    Anti-matroids

  • Gregory Gutin
  • Anders Yeo
    • Categories Approximation Algorithms, Combinatorial Optimization, Graphs and Matroids Tags , ,

    We introduce an anti-matroid as a family $\cal F$ of subsets of a ground set $E$ for which there exists an assignment of weights to the elements of $E$ such that the greedy algorithm to compute a maximal set (with respect to inclusion) in $\cal F$ of minimum weight finds, instead, the unique maximal set … Read more

    On the Riemannian Geometry Defined by Self-Concordant Barriers and Interior-Point Methods

  • Yurii Nesterov
  • Michael J. Todd
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We consider the Riemannian geometry defined on a convex set by the Hessian of a self-concordant barrier function, and its associated geodesic curves. These provide guidance for the construction of efficient interior-point methods for optimizing a linear function over the intersection of the set with an affine manifold. We show that algorithms that follow the … Read more

    The Robust Shortest Path Problem with Interval Data

  • Oya Ekin Karasan
  • Mustafa C. Pinar
  • Hande Yaman
    • Categories Network Optimization, Robust Optimization, Telecommunications Tags , , ,

    Motivated by telecommunication applications, we investigate the shortest path problem on directed acyclic graphs under arc length uncertainties represented as interval numbers. Using a minimax-regret criterion we define and identify robust paths via mixed-integer programming and exploiting interesting structural properties of the problem. Citation Bilkent University, Department of Industrial Engineering, Technical Report August 2001 Article … Read more