constrained optimization

Modified Line Search Sequential Quadratic Methods for Equality-Constrained Optimization with Unified Global and Local Convergence Guarantees

  • Albert S. Berahas
  • Raghu Bollapragada
  • Jiahao Shi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Other Topics Tags , ,

    In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified line search strategy that utilizes second-order information of both the objective and constraint functions, as required, to mitigate the Maratos effect. Contrary … Read more

    Unifying nonlinearly constrained nonconvex optimization

  • Charlie Vanaret
  • Sven Leyffer
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark Tags , , , , , , , , ,

    Derivative-based iterative methods for nonlinearly constrained non-convex optimization usually share common algorithmic components, such as strategies for computing a descent direction and mechanisms that promote global convergence. Based on this observation, we introduce an abstract framework based on four common ingredients that describes most derivative-based iterative methods and unifies their workflows. We then present Uno, … Read more

    Nonlinear Derivative-free Constrained Optimization with a Mixed Penalty-Logarithmic Barrier Approach and Direct Search

  • Andrea Brilli
  • Ana Luisa Custódio
  • Giampaolo Liuzzi
  • Everton Silva
    • Categories Constrained Nonlinear Optimization Tags , , ,

    In this work, we propose the joint use of a mixed penalty-logarithmic barrier approach and generating set search, for addressing nonlinearly constrained derivative-free optimization problems. A merit function is considered, wherein the set of inequality constraints is divided into two groups: one treated with a logarithmic barrier approach, and another, along with the equality constraints, … Read more

    An Inexact Restoration Direct Multisearch Filter Approach to Multiobjective Constrained Derivative-free Optimization

  • Everton Silva
  • Ana Luisa Custódio
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , , ,

    Direct Multisearch (DMS) is a well-established class of methods for multiobjective derivative-free optimization, where constraints are addressed by an extreme barrier approach, only evaluating feasible points. In this work, we propose a filter approach, combined with an inexact feasibility restoration step, to address constraints in the DMS framework. The filter approach treats feasibility as an … Read more

    Fidelity and interruption control for expensive constrained multi-fidelity blackbox optimization

  • Xavier Lebeuf
  • Sébastien Le Digabel
  • Charles Audet
  • Miguel Diago
  • Stéphane Alarie
    • Categories Constrained Nonlinear Optimization, Energy, Optimization of Simulated Systems Tags , , , , ,

    This work introduces a novel blackbox optimization algorithm for computationally expensive constrained multi-fidelity problems. When applying a direct search method to such problems, the scarcity of feasible points may lead to numerous costly evaluations spent on infeasible points. Our proposed fidelity and interruption controlled optimization algorithm addresses this issue by leveraging multi-fidelity information, allowing for … Read more

    First-Order Methods for Nonsmooth Nonconvex Functional Constrained Optimization with or without Slater Points

  • Zhichao Jia
  • Benjamin Grimmer
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show a simple first-order method finds a feasible, ϵ-stationary point at a convergence rate of O(ϵ−4) without relying on compactness or Constraint Qualification (CQ). When CQ holds, this convergence is measured by … Read more

    An Adaptive Sampling Sequential Quadratic Programming Method for Equality Constrained Stochastic Optimization

  • Albert S. Berahas
  • Raghu Bollapragada
  • Baoyu Zhou
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue of dynamic sample selection in the evaluation of the gradient in conjunction with inexact solutions to the SQP subproblems. Under reasonable … Read more

    Handling of constraints in multiobjective blackbox optimization

  • Jean Bigeon
  • Sébastien Le Digabel
  • Ludovic Salomon
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm for single-objective constrained optimization. The constraints are aggregated into a single constraint violation function which is used either in a two-phase approach, where research of a feasible … Read more

    A sequential adaptive regularisation using cubics algorithm for solving nonlinear equality constrained optimization

  • Yonggang Pei
  • Shaofang Song
  • Zhu Detong
    • Categories Constrained Nonlinear Optimization Tags , , ,

    The adaptive regularisation algorithm using cubics (ARC) is initially proposed for unconstrained optimization. ARC has excellent convergence properties and complexity. In this paper, we extend ARC to solve nonlinear equality constrained optimization and propose a sequential adaptive regularisation using cubics algorithm inspired by sequential quadratic programming (SQP) methods. In each iteration of our method, the … Read more

    An active signature method for constrained abs-linear minimization

  • Timo Kreimeier
  • Andrea Walther
  • Andreas Griewank
    • Categories Nonsmooth Optimization Tags , , , , ,

    In this paper we consider the solution of optimization tasks with a piecewise linear objective function and piecewise linear constraints. First, we state optimality conditions for that class of problems using the abs-linearization approach and prove that they can be verified in polynomial time. Subsequently, we propose an algorithm called Constrained Active Signature Method that … Read more