Global Optimization

Simulation Optimization for the Stochastic Economic Lot Scheduling Problem with Sequence-Dependent Setup Times

  • Nils Löhndorf
  • Stefan Minner
  • Manuel Riel
    • Categories Optimization of Simulated Systems, Scheduling, Stochastic Approaches Tags , , , , ,

    We consider the stochastic economic lot scheduling problem (SELSP) with lost sales and random demand, where switching between products is subject to sequence-dependent setup times. We propose a solution based on simulation optimization using an iterative two-step procedure which combines global policy search with local search heuristics for the traveling salesman sequencing subproblem. To optimize … Read more

    A Generalization of a Theorem of Arrow, Barankin and Blackwell to a Nonconvex Case

  • Refail Kasimbeyli
  • Musa Mammadov
    • Categories Global Optimization, Global Optimization Theory, Multi-Criteria Optimization Tags , , , , , ,

    The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a reflexive Banach space partially ordered by a Bishop–Phelps cone. Citation Department of … Read more

    On RIC bounds of Compressed Sensing Matrices for Approximating Sparse Solutions Using Lq Quasi Norms

  • Sheu Ruey-Lin
  • Hsia Yong
    • Categories Basic Sciences Applications, Global Optimization Theory, Nonsmooth Optimization Tags , , ,

    This paper follows the recent discussion on the sparse solution recovery with quasi-norms Lq; q\in(0,1) when the sensing matrix possesses a Restricted Isometry Constant \delta_{2k} (RIC). Our key tool is an improvement on a version of “the converse of a generalized Cauchy-Schwarz inequality” extended to the setting of quasi-norm. We show that, if \delta_{2k}\le 1/2, … Read more

    Branch-and-Lift Algorithm for Deterministic Global Optimization in Nonlinear Optimal Control

  • Benoit Chachuat
  • Boris Houska
    • Categories Global Optimization Theory, Systems governed by Differential Equations Optimization

    This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a spatial branch-and-bound algorithm. A new operation, called lifting, is introduced which refines the control parameterization via a Gram-Schmidt orthogonalization … Read more

    A Probabilistic-Driven Search Algorithm for solving a Class of Optimization Problems

  • Nguyen Huu Thong
    • Categories Global Optimization, Nonlinear Optimization, Robust Optimization Tags ,

    In this paper we introduce a new numerical optimization technique, a Probabilistic-Driven Search Algorithm. This algorithm has the following characteristics: 1) In each iteration of loop, the algorithm just changes the value of k variables to find a new solution better than the current one; 2) In each variable of the solution of the problem, … Read more

    On valid inequalities for quadratic programming with continuous variables and binary indicators

  • Hongbo Dong
  • Jeff Linderoth
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Quadratic Programming Tags ,

    In this paper we study valid inequalities for a fundamental set that involves a continuous vector variable x in [0,1]^n, its associated quadratic form x x’ and its binary indicators. This structure appears when deriving strong relaxations for mixed integer quadratic programs (MIQPs). We treat valid inequalities for this set as lifted from QPB, which … Read more

    An Efficient Global Optimization Algorithm for Nonlinear Sum-of-Ratios Problems

  • Yun-Chol Jong
    • Categories Global Optimization Tags , , , ,

    This paper presents a practical method for finding the globally optimal solution to nonlinear sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to the non-convex nature of this problem, our approach provides a theoretical guarantee of global optimality. Our algorithm is based on … Read more

    A new Search via Probability Algorithm for solving Engineering Optimization Problems

  • Nguyen Huu Thong
    • Categories Applications - Science and Engineering, Global Optimization, Stochastic Programming Tags , , ,

    The Search Algorithms have been introduced in the paper [3][6] under the name ‘Search via Probability Algorithm’. These optimization techniques converge very fast and are very efficient for solving optimization problems with very large scale feasible domains. But these optimization techniques are not effective in solving the numerical optimization problems with long narrow feasible domains. … Read more

    Aircraft deconfliction with speed regulation: new models from mixed-integer optimization

  • Sonia Cafieri
  • Nicolas Durand
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , , ,

    Detecting and solving aircraft conflicts, which occur when aircraft sharing the same airspace are too close to each other according to their predicted trajectories, is a crucial problem in Air Traffic Management. We focus on mixed-integer optimization models based on speed regulation. We first solve the problem to global optimality by means of an exact … Read more

    Analytical formulas for calculating extremal ranks and inertias of quadratic matrix-valued functions

  • Yongge Tian
    • Categories Global Optimization, Nonlinear Optimization, Semi-definite Programming

    group of analytical formulas formulas for calculating the global maximal and minimal ranks and inertias of the quadratic matrix-valued function $$ \phi(X) = \left(\, AXB + C\,\right)\!M\!\left(\, AXB + C \right)^{*} + D $$ are established and their consequences are presented, where $A$, $B$, $C$ and $D$ are given complex matrices with $A$ and $C$ … Read more