Quadratic Programming

Parallel Interior Point Solver for Structured Quadratic Programs: Application to Financial Planning Problems

  • Jacek Gondzio
  • Andreas Grothey
    • Categories Finance and Economics, Parallel Algorithms, Quadratic Programming

    Issues of implementation of a library for parallel interior-point methods for quadratic programming are addressed. The solver can easily exploit any special structure of the underlying optimization problem. In particular, it allows a nested embedding of structures and by this means very complicated real-life optimization problems can be modeled. The efficiency of the solver is … Read more

    Gradient Projection Methods for Quadratic Programs and Applications in Training Support Vector Machines

  • Thomas Serafini
  • Luca Zanni
  • Gaetano Zanghirati
    • Categories Data-Mining, Quadratic Programming Tags , , , ,

    Gradient projection methods based on the Barzilai-Borwein spectral steplength choices are considered for quadratic programming problems with simple constraints. Well known nonmonotone spectral projected gradient methods and variable projection methods are discussed. For both approaches the behavior of different combinations of the two spectral steplengths is investigated. A nw adaptive stplength alternating rule is proposed, … Read more

    Rebalancing an Investment Portfolio in the Presence of Transaction Costs

  • Stephen E. Braun
  • John E. Mitchell
    • Categories Finance and Economics, Quadratic Programming Tags , , ,

    The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an extension of the standard portfolio problem in which transaction costs are incurred to rebalance an investment portfolio. The Markowitz framework of mean-variance efficiency is used with costs modelled as a percentage of the value transacted. … Read more

    Sufficient Global Optimality Conditions for Bivalent Quadratic Optimization

  • Mustafa C. Pinar
    • Categories 0-1 Programming, Quadratic Programming Tags , ,

    We prove a sufficient global optimality condition for quadratic optimization with quadratic constraints where the variables are allowed to take -1 and 1 values. We extend the condition to quadratic programs with matrix variables and orthogonality conditions, and in particular, to the quadratic assignment problem. Citation Bilkent University Technical Report, September 2002. Article Download View … Read more

    On graphs with stability number equal to the optimal value of a convex quadratic program

  • Domingos M. Cardoso
    • Categories Graphs and Matroids, Quadratic Programming

    Since the Motzkin-Straus result on the clique number of graphs, published in 1965, where they show that the size of the largest clique in a graph can be obtained by solving a quadratic programming problem, several results on the continuous approach to the determination of the clique number of a graph or, equivalently, to the … Read more

    Constructing Approximations to the Efficient Set of Convex Quadratic Multiobjective Problems

  • Jörg Fliege
  • Andree Heseler
    • Categories Multi-Criteria Optimization, Quadratic Programming Tags , ,

    In multicriteria optimization, several objective functions have to be minimized simultaneously. For this kind of problem, no single solution can adequately represent the whole set of optimal points. We propose a new efficient method for approximating the solution set of a convex quadratic multiobjective programming problem. The method is based on a warm-start interior point … Read more

    A Comparative Study of Large-Scale Nonlinear Optimization Algorithms

  • Hande Benson
  • David F. Shanno
  • Robert J. Vanderbei
    • Categories Constrained Nonlinear Optimization, Quadratic Programming, Unconstrained Optimization Tags , ,

    In recent years, much work has been done on implementing a variety of algorithms in nonlinear programming software. In this paper, we analyze the performance of several state-of-the-art optimization codes on large-scale nonlinear optimization problems. Extensive numerical results are presented on different classes of problems, and features of each code that make it efficient or … Read more

    Object-Oriented Software for Quadratic Programming

  • Michael Gertz
  • Stephen Wright
    • Categories Optimization Software Design Principles, Quadratic Programming Tags , ,

    We describe the object-oriented software package OOQP for solving convex quadratic programming problems (QP). The primal-dual interior point algorithms supplied by OOQP are implemented in a way that is largely independent of the problem structure. Users may exploit problem structure by supplying linear algebra, problem data, and variable classes that are customized to their particular … Read more

    New Results on Quadratic Minimization

  • Yinyu Ye
  • Shuzhong Zhang
    • Categories Quadratic Programming, Semi-definite Programming Tags , ,

    In this paper we present several new results on minimizing an indefinite quadratic function under quadratic/linear constraints. The emphasis is placed on the case where the constraints are two quadratic inequalities. This formulation is known as {\em the extended trust region subproblem}\/ and the computational complexity of this problem is still unknown. We consider several … Read more