Constrained Nonlinear Optimization

An Augmented Lagrangian Proximal Alternating Method for Sparse Discrete Optimization Problems

  • Xiaoliang Song
  • Yue Teng
  • Li Yang
  • Bo Yu
    • Categories Approximation Algorithms, Constrained Nonlinear Optimization, Finance and Economics

    In this paper, an augmented Lagrangian proximal alternating (ALPA) method is proposed for two class of large-scale sparse discrete constrained optimization problems in which a sequence of augmented Lagrangian subproblems are solved by utilizing proximal alternating linearized minimization framework and sparse projection techniques. Under the Mangasarian-Fromovitz and the basic constraint qualification, we show that any … Read more

    Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method

  • Shafiu Jibrin
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Semi-definite Programming Tags , ,

    We study the problem of computing weighted analytic center for system of linear matrix inequality constraints. The problem can be solved using the Standard Newton’s method. However, this approach requires that a starting point in the interior point of the feasible region be given or a Phase I problem be solved. We address the problem … Read more

    Some theoretical limitations of second-order algorithms for smooth constrained optimization

  • Gabriel Haeser
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In second-order algorithms, we investigate the relevance of the constant rank of the full set of active constraints in ensuring global convergence to a second-order stationary point. We show that second-order stationarity is not expected in the non-constant rank case if the growth of the so-called tangent multipliers, associated with a second-order complementarity measure, is … Read more

    A Penalty Method for Rank Minimization Problems in Symmetric Matrices

  • John E. Mitchell
  • Xin Shen
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Semi-definite Programming Tags , ,

    The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive semidefinite matrices to be complementary. We investigate calmness of locally optimal solutions to the SDCMPCC formulation and hence show that any locally optimal … Read more

    Complexity Analysis of a Trust Funnel Algorithm for Equality Constrained Optimization

  • Frank E. Curtis
  • Daniel P. Robinson
  • Mohammadreza Samadi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , ,

    A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an $\epsilon$-feasible point and a second phase to seek optimality while maintaining at least $\epsilon$-feasibility. A two-phase approach of this kind based on … Read more

    Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points

  • Ernesto G. Birgin
  • Gabriel Haeser
  • Alberto Ramos
    • Categories Constrained Nonlinear Optimization Tags , ,

    Augmented Lagrangian methods with convergence to second-order stationary points in which any constraint can be penalized or carried out to the subproblems are considered in this work. The resolution of each subproblem can be done by any numerical algorithm able to return approximate second-order stationary points. The developed global convergence theory is stronger than the … Read more

    A parallelizable augmented Lagrangian method applied to large-scale non-convex-constrained optimization problems

  • Natashia Boland
  • Brian Dandurand
  • Andrew C. Eberhard
  • Fabricio Oliveira
  • Jeffrey Christiansen
    • Categories (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization, Parallel Algorithms Tags , , , ,

    We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is compact but not necessarily convex. Such problems arise, for example, in the split-variable deterministic reformulation of stochastic mixed-integer optimization problems. The dual solution approach needs … Read more

    Efficient solution of quadratically constrained quadratic subproblems within the MADS algorithm

  • Nadir Amaioua
  • Charles Audet
  • Andrew R. Conn
  • Sébastien Le Digabel
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization

    The Mesh Adaptive Direct Search algorithm (MADS) is an iterative method for constrained blackbox optimization problems. One of the optional MADS features is a versatile search step in which quadratic models are built leading to a series of quadratically constrained quadratic subproblems. This work explores different algorithms that exploit the structure of the quadratic models: … Read more

    Numerical solution of optimal control problems with explicit and implicit switches

  • Hans Georg Bock
  • Christian Kirches
  • Andreas Meyer
  • Andreas Potschka
    • Categories Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization

    In this article, we present a unified framework for the numerical solution of optimal control problems constrained by ordinary differential equations with both implicit and explicit switches. We present the problem class and qualify different types of implicitly switched systems. This classification significantly affects opportunities for solving such problems numerically. By using techniques from generalized … Read more

    Sequential Linear Programming and Particle Swarm Optimization for the optimization of energy districts

  • Stefania Bellavia
  • Elisa Riccietti
  • Stefano Sello
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    In this paper we deal with the optimization of energy resources management of industrial districts, with the aim of minimizing the customer energy expenses. In a district the number of possible energy system combinations is really large, and a manual design approach might lead to a suboptimal solution. For this reason we designed a software … Read more