Month: June 2010

Multistage Stochastic Portfolio Optimisation in Deregulated Electricity Markets Using Linear Decision Rules

  • Daniel Kuhn
  • Paula Rocha
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean-variance optimisation model for the management of … Read more

    Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions

  • Samir Adly
  • Abderrahim Hantoute
  • Michel Thera
    • Categories Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization Tags , , , , , ,

    The main objective of this paper is to provide new explicit criteria to characterize weak lower semi-continuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by the means of the proximal … Read more

    A Retrospective Filter Trust Region Algorithm For Unconstrained Optimization

  • Zhongwen Chen
  • Yue Lu
    • Categories Unconstrained Optimization Tags , , ,

    In this paper, we propose a retrospective filter trust region algorithm for unconstrained optimization, which is based on the framework of the retrospective trust region method and associated with the technique of the multi dimensional filter. The new algorithm gives a good estimation of trust region radius, relaxes the condition of accepting a trial step … Read more

    Copositivity and constrained fractional quadratic problems

  • Paula Alexandra Amaral
  • Immanuel M. Bomze
  • Joaquim J. Júdice
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Linear, Cone and Semidefinite Programming

    We provide Completely Positive and Copositive Programming formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming (SDP) relaxations are derived for finding good lower bounds to these fractional programs, which are used in a global optimization branch-and-bound approach. Applications of the CFQP and StFQP, … Read more

    Direct Multisearch for Multiobjective Optimization

  • Ana Luisa Custódio
  • A. Ismael F. Vaz
  • Luis Nunes Vicente
  • J. F. A. Madeira
    • Categories Multi-Criteria Optimization Tags , , , , , , ,

    In practical applications of optimization it is common to have several conflicting objective functions to optimize. Frequently, these functions are subject to noise or can be of black-box type, preventing the use of derivative-based techniques. We propose a novel multiobjective derivative-free methodology, calling it direct multisearch (DMS), which does not aggregate any of the objective … Read more

    Explicit Convex and Concave Envelopes through Polyhedral Subdivisions

  • Jean-Philippe P. Richard
  • Mohit Tawarmalani
  • Chuanhui Xiong
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Polyhedra Tags , ,

    In this paper, we derive explicit characterizations of convex and concave envelopes of several nonlinear functions over various subsets of a hyper-rectangle. These envelopes are obtained by identifying polyhedral subdivisions of the hyper-rectangle over which the envelopes can be constructed easily. In particular, we use these techniques to derive, in closed-form, the concave envelopes of … Read more

    Worst Case Complexity of Direct Search

  • Luis Nunes Vicente
    • Categories Nonlinear Optimization Tags , , ,

    In this paper we prove that direct search of directional type shares the worst case complexity bound of steepest descent when sufficient decrease is imposed using a quadratic function of the step size parameter. This result is proved under smoothness of the objective function and using a framework of the type of GSS (generating set … Read more

    Bilevel Derivative-Free Optimization and its Application to Robust Optimization

  • Andrew R. Conn
  • Luis Nunes Vicente
    • Categories Nonlinear Optimization Tags , , , , ,

    We address bilevel programming problems when the derivatives of both the upper and the lower level objective functions are unavailable. The core algorithms used for both levels are trust-region interpolation-based methods, using minimum Frobenius norm quadratic models when the number of points is smaller than the number of basis components. We take advantage of the … Read more

    A heuristic approach for packing rectangles in convex regions.

  • Andrea Cassioli
  • Marco Locatelli
    • Categories Applications - OR and Management Sciences, Global Optimization, Nonlinear Optimization Tags , , ,

    In this paper we propose a heuristic approach for the problem of packing equal rectangles within a convex region. The approach is based on an Iterated Local Search scheme (or, using a terminology employed for continuous problems, a Monotonic Basin Hopping), in which the key step is the perturbation move. Different perturbation moves, both combinatorial … Read more

    A probabilistic comparison of split and type 1 triangle cuts for two row mixed-integer programs

  • Shabbir Ahmed
  • Qie He
  • George L. Nemhauser
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , , ,

    We provide a probabilistic comparison of split and type 1 triangle cuts for mixed-integer programs with two rows and two integer variables. Under a simple probabilistic model of the problem parameters, we show that a simple split cut, i.e. a Gomory cut, is more likely to be better than a type 1 triangle cut in … Read more