Constrained Nonlinear Optimization

General Perturbation Resilient Dynamic String-Averaging for Inconsistent Problems with Superiorization

  • Kay Barshad
  • Yair Censor
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , , , , , , , , ,

    In this paper we introduce a General Dynamic String-Averaging (GDSA) iterative scheme and investigate its convergence properties in the inconsistent case, that is, when the input operators don’t have a common fixed point. The Dynamic String-Averaging Projection (DSAP) algorithm itself was introduced in an 2013 paper, where its strong convergence and bounded perturbation resilience were … Read more

    First-order methods for stochastic and finite-sum convex optimization with deterministic constraints

  • Zhaosong Lu
  • Yifeng Xiao
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Stochastic Programming Tags , , , , , ,

    In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an \(\epsilon\)-expectedly feasible stochastic optimal solution, in which the expected constraint violation and expected optimality gap are both within a prescribed tolerance ϵ. However, in many practical applications, constraints must be nearly … Read more

    Efficient QUIC-Based Damped Inexact Iterative Reweighting for Sparse Inverse Covariance Estimation with Nonconvex Partly Smooth Regularization

  • Xiangyu Yang
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization, Semi-definite Programming Tags , , ,

    In this paper, we study sparse inverse covariance matrix estimation incorporating partly smooth nonconvex regularizers. To solve the resulting regularized log-determinant problem, we develop DIIR-QUIC—a novel Damped Inexact Iteratively Reweighted algorithm based on QUadratic approximate Inverse Covariance (QUIC) method. Our approach generalizes the classic iteratively reweighted \(\ell_1\) scheme through damped fixed-point updates. A key novelty … Read more

    Retrospective Approximation Sequential Quadratic Programming for Stochastic Optimization with General Deterministic Nonlinear Constraints

  • Shagun Gupta
  • Raghu Bollapragada
  • Albert S. Berahas
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

    In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially constructs increasingly accurate approximations of the true problems which are solved to a specified accuracy via a deterministic solver, thereby decoupling the uncertainty from … Read more

    An adaptive single-loop stochastic penalty method for nonconvex constrained stochastic optimization

  • Shiji Zuo
  • Xiao Wang
  • Hao Wang
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    Adaptive update schemes for penalty parameters are crucial to enhancing robustness and practical applicability of penalty methods for constrained optimization. However, in the context of general constrained stochastic optimization, additional challenges arise due to the randomness introduced by adaptive penalty parameters. To address these challenges, we propose an Adaptive Single-loop Stochastic Penalty method (AdaSSP) in … Read more

    Sensitivity analysis for parametric nonlinear programming: A tutorial

  • François Pacaud
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags ,

    This tutorial provides an overview of the current state-of-the-art in the sensitivity analysis for nonlinear programming. Building upon the fundamental work of Fiacco, it derives the sensitivity of primal-dual solutions for regular nonlinear programs and explores the extent to which Fiacco’s framework can be extended to degenerate nonlinear programs with non-unique dual solutions. The survey … Read more

    The improvement function in branch-and-bound methods for complete global optimization

  • Stefan Schwarze
  • Oliver Stein
  • Peter Kirst
    • Categories Constrained Nonlinear Optimization, Global Optimization Tags , , , ,

    We present a new spatial branch-and-bound approach for treating optimization problems with nonconvex inequality constraints. It is able to approximate the set of all global minimal points in case of solvability, and else to detect infeasibility. The new technique covers the nonconvex constraints by means of an improvement function which, although nonsmooth, can be treated … Read more

    IPAS: An Adaptive Sample Size Method for Weighted Finite Sum Problems with Linear Equality Constraints

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Sanja Rapajić
  • Luka Rutešić
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic optimization method is proposed. The method belongs to the class of variable sample size first order methods, … Read more

    The improvement function reformulation for graphs of minimal point mappings

  • Stefan Schwarze
  • Oliver Stein
    • Categories Constrained Nonlinear Optimization, Game Theory, Global Optimization Theory Tags , , , , ,

    Graphs of minimal point mappings of parametric optimization problems appear in the definition of feasible sets of bilevel optimization problems and of semi-infinite optimization problems, and the intersection of multiple such graphs defines (generalized) Nash equilibria. This paper shows how minimal point graphs of nonconvex parametric optimization problems can be written with the help of … Read more

    Superiorization and Perturbation Resilience of Algorithms: A Continuously Updated Bibliography

  • Yair Censor
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , ,

    This document presents a (mostly) chronologically-ordered bibliography of scientific publications on the superiorization methodology and perturbation resilience of algorithms which is compiled and continuously updated by us at: http://math.haifa.ac.il/yair/bib-superiorization-censor.html. Since the beginnings of this topic we try to trace the work that has been published about it since its inception. To the best of our … Read more