Other Topics

Linear-quadratic control problem with a linear term on semiinfinite interval:theory and applications

  • Leonid Faybusovich
  • Thanasak Mouktonglang
    • Categories Control Applications, Infinite Dimensional Optimization, Multi-Criteria Optimization Tags , ,

    We describe a complete solution of the linear-quaratic control problem with the linear term in the objective function on a semiinfinite interval. This problem has important applications to calculation of Nesterov-Todd and other primal-dual directions in infinite-dimensional setting. Citation Technical report, University of Notre Dame, December, 2003 Article Download View Linear-quadratic control problem with a … Read more

    Inferring efficient weights from pairwise comparison matrices

  • Rafael Blanquero
  • Emilio Carrizosa
  • E. Conde
    • Categories Multi-Criteria Optimization Tags , , ,

    Several Multi-Criteria-Decision-Making methodologies assume the existence of weights associated with the different criteria, reflecting their relative importance. One of the most popular ways to infer such weights is the Analytic Hierarchy Process, which constructs first a matrix of pairwise comparisons, from which weights are derived following one out of many existing procedures, such as the … Read more

    Envelope Theorems For Finite Choice Sets

  • Somdeb Lahiri
    • Categories Finance and Economics, Game Theory, Multi-Criteria Optimization Tags , , ,

    This paper is concerned with the study of envelope theorems for finite choice sets. More specifically, we consider the problem of differentiability of the value function arising out of the maximization of a parametrized objective function, when the set of alternatives is non-empty and finite. The parameter is confined to the closed interval [0,1] and … Read more

    Characterizing polynomials with roots in a semi-algebraic set

  • Jean-Bernard Lasserre
    • Categories Control Applications, Other Topics

    Consider a real polynomial $p$ and a semi-algebraic subset $S$ of the complex plane, defined by finitely many polynomial inequalities $g_k(z,\bar{z}) \geq 0$ for some complex polynomials $\{g_k\}$. We provide necessary and sufficient conditions on the coefficients of $p$ for the zeros of $p$ to be in $S$. Citation IEEE Trans. Automatic Control 49 (2004), … Read more

    Stable Matchings for A Generalized Marriage Problem

  • Somdeb Lahiri
    • Categories Finance and Economics, Game Theory Tags , , , ,

    We show that a simple genralization of the Deferred Acceptance Procedure with men proposing due to Gale and Shapley(1962), yeilds outcomes for a generalized marriage problem, which are necessarily stable. We also show, that any outcome of this prcedure is Weakly Pareto Optimal for Men, i.e., there is no other outcome which all men prefer … Read more

    Interior-Point Algorithms, Penalty Methods and Equilibrium Problems

  • Hande Benson
  • Arun Sen
  • David F. Shanno
  • Robert J. Vanderbei
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Game Theory Tags , , , ,

    In this paper we consider the question of solving equilibrium problems—formulated as complementarity problems and, more generally, mathematical programs with equilibrium constraints (MPEC’s)—as nonlinear programs, using an interior-point approach. These problems pose theoretical difficulties for nonlinear solvers, including interior-point methods. We examine the use of penalty methods to get around these difficulties, present an example … Read more

    A Multicriteria Approach to Bilevel Optimization

  • Jörg Fliege
  • Luis Nunes Vicente
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags ,

    In this paper we study the relationship between bilevel optimization and bicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower level problem of the bilevel optimization problem … Read more

    Stable Sets of Weak Tournaments

  • Somdeb Lahiri
    • Categories Applications - OR and Management Sciences, Game Theory, Multi-Criteria Optimization Tags ,

    The purpose of this paper is to obtain conditions on weak tournaments, which guarantee that every non-empty subset of alternatives admits a stable set. We show that every stable set always contains the core. We also show that there exists a unique stable set for each non-empty subset of alternatives which coincides with its core … Read more

    Solving Method for a Class of Bilevel Linear Programming based on Genetic Algorithms

  • Zhong-Ping Wan
  • Guang-Min Wang
  • Xian-Jia Wang
    • Categories Linear, Cone and Semidefinite Programming, Multi-Criteria Optimization, Nonlinear Optimization Tags , ,

    The paper studies and designs an genetic algorithm (GA) of the bilevel linear programming problem (BLPP) by constructing the fitness function of the upper-level programming problem based on the definition of the feasible degree. This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into … Read more

    Optimization problems with equilibrium constraints and their numerical solution

  • Michal Kočvara
  • Jiri V. Outrata
    • Categories Complementarity and Variational Inequalities, Nonlinear Optimization, Other Topics Tags

    We consider a class of optimization problems with a generalized equation among the constraints. This class covers several problem types like MPEC (Mathematical Programs with Equilibrium Constraints) and MPCC (Mathematical Programs with Complementarity Constraints). We briefly review techniques used for numerical solution of these problems: penalty methods, nonlinear programming (NLP) techniques and Implicit Programming approach … Read more