Constrained Nonlinear Optimization

Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Bound-constrained Optimization, Constrained Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , ,

    Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in … Read more

    A pattern search and implicit filtering algorithm for solving linearly constrained minimization problems with noisy objective functions

  • Maria A. Diniz-Ehrhardt
  • Sandra Augusta Santos
  • D. G. Ferreira
    • Categories Constrained Nonlinear Optimization

    PSIFA -Pattern Search and Implicit Filtering Algorithm- is a derivative-free algorithm that has been designed for linearly constrained problems with noise in the objective function. It combines some elements of the pattern search approach of Lewis and Torczon (2000) with ideas from the method of implicit filtering of Kelley (2011) enhanced with a further analysis … Read more

    The New Butterfly Relaxation Methods for Mathematical Program with Complementarity Constraints

  • Jean-Pierre Dussault
  • Tangi Migot
  • Mounir Haddou
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization Tags

    We propose a new family of relaxation schemes for mathematical program with complementarity constraints that extends the relaxations of Kadrani, Dussault, Bechakroun from 2009 and the one of Kanzow \& Schwartz from 2011. We discuss the properties of the sequence of relaxed non-linear program as well as stationarity properties of limiting points. A sub-family of … Read more

    How to Compute a M-stationary point of the MPCC

  • Jean-Pierre Dussault
  • Tangi Migot
  • Mounir Haddou
  • Abdeslam Kadrani
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization

    We discuss here the convergence of relaxation methods for MPCC with approximate sequence of stationary points by presenting a general framework to study these methods. It has been pointed out in the literature, \cite{kanzow2015}, that relaxation methods with approximate stationary points fail to give guarantee of convergence. We show that by defining a new strong … Read more

    Iteration-complexity of a Jacobi-type non-Euclidean ADMM for multi-block linearly constrained nonconvex programs

  • Jefferson Gonçalves Melo
  • Renato D.C. Monteiro
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    This paper establishes the iteration-complexity of a Jacobi-type non-Euclidean proximal alternating direction method of multipliers (ADMM) for solving multi-block linearly constrained nonconvex programs. The subproblems of this ADMM variant can be solved in parallel and hence the method has great potential to solve large scale multi-block linearly constrained nonconvex programs. Moreover, our analysis allows the … Read more

    Exact augmented Lagrangian functions for nonlinear semidefinite programming

  • Ellen H. Fukuda
  • Bruno F. Lourenço
    • Categories Constrained Nonlinear Optimization, Semi-definite Programming Tags , ,

    In this paper, we study augmented Lagrangian functions for nonlinear semidefinite programming (NSDP) problems with exactness properties. The term exact is used in the sense that the penalty parameter can be taken appropriately, so a single minimization of the augmented Lagrangian recovers a solution of the original problem. This leads to reformulations of NSDP problems … Read more

    A Primal-Dual Augmented Lagrangian Penalty-Interior-Point Filter Line Search Algorithm

  • Christof Büskens
  • Renke Kuhlmann
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    Interior-point methods have been shown to be very efficient for large-scale nonlinear programming. The combination with penalty methods increases their robustness due to the regularization of the constraints caused by the penalty term. In this paper a primal-dual penalty-interior-point algorithm is proposed, that is based on an augmented Lagrangian approach with an l2-exact penalty function. … Read more

    A Derivative-Free and Ready-to-Use NLP Solver for Matlab or Octave

  • Florian Jarre
  • Felix Lieder
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization Software and Modeling Systems Tags , ,

    This paper introduces a derivative-free and ready-to-use solver for nonlinear programs with nonlinear equality and inequality constraints (NLPs). Using finite differences and a sequential quadratic programming (SQP) approach, the algorithm aims at finding a local minimizer and no extra attempt is made to generate a globally optimal solution. Due to the use of finite differences, … Read more

    Outer-Product-Free Sets for Polynomial Optimization and Oracle-Based Cuts

  • Daniel Bienstock
  • Chen Chen
  • Gonzalo Muñoz
    • Categories Constrained Nonlinear Optimization, Cutting Plane Approaches, Global Optimization Theory Tags , ,

    Cutting planes are derived from specific problem structures, such as a single linear constraint from an integer program. This paper introduces cuts that involve minimal structural assumptions, enabling the generation of strong polyhedral relaxations for a broad class of problems. We consider valid inequalities for the set $S\cap P$, where $S$ is a closed set, … Read more

    Bilevel optimization with a multiobjective problem in the lower level

  • Roberto Andreani
  • Sandra Augusta Santos
  • Viviana A. Ramirez
  • Leonardo D. Secchin
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

    Bilevel problems model instances with a hierarchical structure. Aiming at an efficient solution of a constrained multiobjective problem according with some pre-defined criterion, we reformulate this optimization but non standard problem as a classic bilevel one. This reformulation intents to encompass all the objectives, so that the properly efficient solution set is recovered by means … Read more