On the Relationship between Bilevel Decomposition Algorithms and Direct Interior-Point Methods

  • Victor DeMiguel
  • Francisco Javier Nogales
    • Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization Tags , , ,

    Engineers have been using \emph{bilevel decomposition algorithms} to solve certain nonconvex large-scale optimization problems arising in engineering design projects. These algorithms transform the large-scale problem into a bilevel program with one upper-level problem (the master problem) and several lower-level problems (the subproblems). Unfortunately, there is analytical and numerical evidence that some of these commonly used … Read more

    A Local Convergence Analysis of Bilevel Decomposition Algorithms

  • Victor DeMiguel
  • Walter Murray
    • Categories Multidisciplinary Design Optimization, Nonlinear Optimization Tags , , ,

    Decomposition algorithms exploit the structure of large-scale optimization problems by breaking them into a set of smaller subproblems and a coordinating master problem. Cutting-plane methods have been extensively used to decompose convex problems. In this paper, however, we focus on certain nonconvex problems arising in engineering. Engineers have been using bilevel decomposition algorithms to tackle … Read more

    An Extension of Sums of Squares Relaxations to Polynomial Optimization Problems over Symmetric Cones

  • Masakazu Kojima
  • Masakazu Muramatsu
    • Categories Global Optimization Theory, Semi-definite Programming Tags , , , , , ,

    This paper is based on a recent work by Kojima which extended sums of squares relaxations of polynomial optimization problems to polynomial semidefinite programs. Let ${\cal E}$ and ${\cal E}_+$ be a finite dimensional real vector space and a symmetric cone embedded in ${\cal E}$; examples of $\calE$ and $\calE_+$ include a pair of the … Read more

    Cutting plane algorithms for robust conic convex optimization

  • Juan Alfredo Gomez
  • Walter Gómez
    • Categories Linear, Cone and Semidefinite Programming, Semi-infinite Programming Tags , ,

    In the paper we study some well-known cases of nonlinear programming problems, presenting them as instances of Inexact Linear Programming. The class of problems considered contains, in particular, semidefinite programming, second order cone programming and special cases of inexact semidefinite programming. Strong duality results for the nonlinear problems studied are obtained via the Lagrangian duality. … Read more

    Three-dimensional quasi-static frictional contact by using second-order cone linear complementarity problem

  • Y. Kanno
  • J.A.C. Martins
  • A. Pinto da Costa
    • Categories Complementarity and Variational Inequalities, Mechanical Engineering, Second-Order Cone Programming

    A new formulation is presented for the three-dimensional incremental quasi-static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a Second-Order Cone Linear omplementarity Problem (SOCLCP) is formulated, which consists of complementarity conditions defined by the bilinear functions and the second-order cone constraints. The equilibrium configurations are obtained by using … Read more

    A comparison of complete global optimization solvers

  • Waltraud Huyer
  • Arnold Neumaier
  • Oleg Shcherbina
  • Tamás Vinkó
    • Categories Global Optimization Tags , , ,

    Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables. Citationsubmitted to the special issue on Global Optimization of Math. ProgrammingArticleDownload View PDF

    Mean-risk objectives in stochastic programming

  • Shabbir Ahmed
    • Categories Nonsmooth Optimization, Stochastic Programming Tags , , ,

    Traditional stochastic programming is risk neutral in the sense that it is concerned with the optimization of an expectation criteria. A common approach to addressing risk in decision making problems is to consider a weighted mean-risk criterion, where some dispersion statistic is used as a measure of risk. We investigate the computational suitability of various … Read more

    Semidefinite descriptions of cones defining spectral mask constraints

  • Leonid Faybusovich
    • Categories Applications - Science and Engineering, Semi-definite Programming Tags , ,

    We discuss in detail an additive structure of cones of trigonometric polynomials nonnegative on the union of finite number of pairwise disjoint segments of the unit circle. We derive new descriptions of these cones in terms of semidefinite constraints. We explain the results of M. Krein and A. Nudelman providing a description of dual cones … Read more

    On Implementing Self-Regular Proximity Based Feasible IPMs

  • Jiming Peng
  • Tamás Terlaky
  • Guoqing Zhang
  • Xiaohang Zhu
    • Categories Linear Programming, Optimization Software Benchmark Tags , ,

    Self-regular based interior point methods present a unified novel approach for solving linear optimization and conic optimization problems. So far it was not known if the new Self-Regular IPMs can lead to similar advances in computational practice as shown in the theoretical analysis. In this paper, we present our experiences in developing the software package … Read more

    A hybrid bin-packing heuristic to multiprocessor scheduling

  • Adriana C. Alvim
  • Celso C. Ribeiro
    • Categories Meta Heuristics, Scheduling Tags , , ,

    The multiprocessor scheduling problem consists in scheduling a set of tasks with known processing times into a set of identical processors so as to minimize their makespan, i.e., the maximum processing time over all processors. We propose a new heuristic for solving the multiprocessor scheduling problem, based on a hybrid heuristic to the bin packing … Read more