Constrained Nonlinear Optimization

Single-Loop Deterministic and Stochastic Interior-Point Algorithms for Nonlinearly Constrained Optimization

  • Frank E. Curtis
  • Qi Wang
  • Xin Jiang
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science

    An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear and/or nonconvex, and when constraint values and derivatives are tractable to compute, but objective function values and derivatives can only be estimated. The algorithm … Read more

    Immunity to Increasing Condition Numbers of Linear Superiorization versus Linear Programming

  • Jan Schröder
  • Yair Censor
  • Philipp Süss
  • Karl-Heinz Küfer
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Linear Programming Tags , , , , , , ,

    Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at finding a point that fulfills the constraints and has the minimal value of the objective function … Read more

    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

    Composite optimization models via proximal gradient method with a novel enhanced adaptive stepsize

  • Pham Thi Hoai
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    We first consider the convex composite optimization models with the local Lipschitzness condition imposed on the gradient of the differentiable term. The classical proximal gradient method will be studied with our novel enhanced adaptive stepsize selection. To obtain the convergence of the proposed algorithm, we establish a sufficient decrease type inequality associated with our new … Read more

    Optimization without Retraction on the Random Generalized Stiefel Manifold

  • Simon Vary
  • Bin Gao
  • Pierre-Antoine Absil
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    Optimization over the set of matrices \(X\) that satisfy \(X^\top B X = I_p\), referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as the canonical correlation analysis (CCA), independent component analysis (ICA), and the generalized eigenvalue problem (GEVP). Solving these problems is typically done by iterative methods … Read more

    Floorplanning with I/O assignment via feasibility-seeking and superiorization methods

  • ShanYu
  • Yair Censor
  • Guojie Luo
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, VLSI layout Tags , , , , , ,

    The feasibility-seeking approach offers a systematic framework for managing and resolving intricate constraints in continuous problems, making it a promising avenue to explore in the context of floorplanning problems with increasingly heterogeneous constraints. The classic legality constraints can be expressed as the union of convex sets. However, conventional projection-based algorithms for feasibility-seeking do not guarantee … Read more

    solar: A solar thermal power plant simulator for blackbox optimization benchmarking

  • Sébastien Le Digabel
  • Charles Audet
  • Xavier Lebeuf
  • Miguel Diago
  • Aïmen E. Gheribi
  • Christophe Tribes
    • Categories Constrained Nonlinear Optimization, Energy, Optimization Software Benchmark Tags , , ,

    This work introduces solar, a collection of  ten optimization problem instances for benchmarking blackbox optimization solvers. The instances present different design aspects of a concentrated solar power plant simulated by blackbox numerical models. The type of variables (discrete or continuous), dimensionality, and number and types of constraints (including hidden constraints)  differ across instances. Some are deterministic, others are stochastic … Read more