ON USING THE ELASTIC MODE IN NONLINEAR PROGRAMMING APPROACHES TO MATHEMATICALPROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags , , , , ,

    We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using algorithms and procedures of smooth nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sucient conditions for their Lagrange multiplier set to be nonempty. MPCCs that have nonempty Lagrange multiplier sets and that satisfy the quadratic growth condition can … Read more

    OPTIMIZATION-BASED SIMULATION OF NONSMOOTH RIGID MULTIBODY DYNAMICS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Mechanical Engineering Tags , , , ,

    We present a time-stepping method to simulate rigid multibody dynamics with inelastic collision, contact, and friction. The method progresses with fixed time step without backtracking for collision and solves at every step a strictly convex quadratic program. We prove that a solution sequence of the method converges to the solution of a measure differential inclusion. … Read more

    Security-constrained transmission planning: A mixed-integer disjunctive approach

  • Laura Bahiense
  • S. Binato
  • G. C. Oliveira
  • Mario Pereira
  • L. Thomé
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences Tags ,

    We extend a static mixed intger diajunctive (MID) transmission expansion planning model so as to deal with circuit contingency criterion. The model simultaneously represents the network constraints for base case and each selected circuit contingency. The MID approach aloows a commercial optimization solver to achieve and prove solution aptimiality. The proposed approach is applied to … Read more

    Stochastic p-Robust Location Problems

  • Mark S. Daskin
  • Lawrence V. Snyder
    • Categories Production and Logistics, Robust Optimization Tags , , ,

    Many objectives have been proposed for optimization under uncertainty. The typical stochastic programming objective of minimizing expected cost may yield solutions that are inexpensive in the long run but perform poorly under certain realizations of the random data. On the other hand, the typical robust optimization objective of minimizing maximum cost or regret tends to … Read more

    Aggregation in Stochastic Dynamic Programming

  • Marina A. Epelman
  • Theodore Lambert
  • Robert L. Smith
    • Categories Dynamic Programming Tags , ,

    We present a general aggregation method applicable to all finite-horizon Markov decision problems. States of the MDP are aggregated into macro-states based on a pre-selected collection of “distinguished” states which serve as entry points into macro-states. The resulting macro-problem is also an MDP, whose solution approximates an optimal solution to the original problem. The aggregation … Read more

    A fictitious play approach to large-scale optimization

  • Marina A. Epelman
  • Theodore Lambert
  • Robert L. Smith
    • Categories Game Theory, Optimization of Simulated Systems Tags ,

    In this paper we investigate the properties of the sampled version of the fictitious play algorithm, familiar from game theory, for games with identical payoffs, and propose a heuristic based on fictitious play as a solution procedure for discrete optimization problems of the form $\max\{u(y):y=(y^1,\ldots,y^n)\in\setY^1\times\cdots\times\setY^n\}$, i.e., in which the feasible region is a Cartesian product … Read more

    On cost matrices with two and three distinct values of Hamiltonian paths and cycles

  • Santosh N. Kabadi
  • Abraham Punnen
    • Categories Approximation Algorithms, Combinatorial Optimization Tags , , ,

    Polynomially testable characterization of cost matrices associated with a complete digraph on $n$ nodes such that all the Hamiltonian cycles (tours) have the same cost is well known. Tarasov~\cite{TARA81} obtained a characterization of cost matrices where tour costs take two distinct values. We provide a simple alternative characterization of such cost matrices that can be … Read more

    Symmetry Points of Convex Set: Basic Properties and Computational Complexity

  • Alexandre Belloni
  • Robert M. Freund
    • Categories Convex and Nonsmooth Optimization, Linear Programming Tags , , ,

    Given a convex body S and a point x \in S, let sym(x,S) denote the symmetry value of x in S: sym(x,S):= max{t : x + t(x – y) \in S for every y \in S}, which essentially measures how symmetric S is about the point x, and define sym(S):=\max{sym(x,S) : x \in S }. … Read more

    Recovering Risk-Neutral Probability Density Functions from Options Prices using Cubic Splines

  • Ana M. Monteiro
  • Reha H. Tütüncü
  • Luis Nunes Vicente
    • Categories Finance and Economics, Quadratic Programming, Semi-definite Programming Tags , , , ,

    We present a new approach to estimate the risk-neutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting optimization problem, used to invert the data and … Read more

    Subspace trust-region methods for large bound-constrained nonlinear equations

  • Stefania Bellavia
  • Benedetta Morini
    • Categories Nonlinear Optimization Tags , , ,

    Trust-region methods for solving large bound-constrained nonlinear systems are considered. They allow for spherical or elliptical trust-regions where the search of an approximate solution is restricted to a low dimensional space. A general formulation for these methods is introduced and global and superlinear/quadratic convergence is shown under standard assumptions. Viable approaches for implementation in conjunction … Read more