Constrained Nonlinear Optimization

Complexity of quadratic penalty methods with adaptive accuracy under a PL condition for the constraints

  • Florentin Goyens
  • Geovani Nunes Grapiglia
    • Categories Constrained Nonlinear Optimization Tags , , ,

    We study the quadratic penalty method (QPM) for smooth nonconvex optimization problems with equality constraints. Assuming the constraint violation satisfies the PL condition near the feasible set, we derive sharper worst-case complexity bounds for obtaining approximate first-order KKT points. When the objective and constraints are twice continuously differentiable, we show that QPM equipped with a … Read more

    A derivative-free trust-region approach for Low Order-Value Optimization problems

  • Francisco N. C. Sobral
  • A. E. Schwertner
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    The Low Order-Value Optimization (LOVO) problem involves minimizing the minimum among a finite number of function values within a feasible set. LOVO has several practical applications such as robust parameter estimation, protein alignment, portfolio optimization, among others. In this work, we are interested in the constrained nonlinear optimization LOVO problem of minimizing the minimum between … Read more

    On the Convergence of Constrained Gradient Method

  • Danqing Zhou
  • Hongmei Chen
  • Shiqian Ma
  • Junfeng Yang
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags ,

    The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence results for CGM, the assumptions employed therein are quite restrictive; in some cases, certain assumptions are mutually inconsistent, leading to gaps in the underlying analysis. This … Read more

    Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems

  • Hussam Al Daas
  • Nicholas I. M. Gould
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems lie on a manifold of approximately very low rank as a function of their controlling parameters (trust-region radius or regularization weight). Based on this, we build a … Read more

    An Exact Penalty Method for Stochastic Equality-Constrained Optimization

  • Yawen Cui
  • Qiankun Shi
  • Xiao Wang
  • Xiantao Xiao
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    In this paper, we study a penalty method for stochastic equality-constrained optimization, where both the objective and constraints are expressed in general expectation form. We introduce a novel adaptive strategy for updating the penalty parameter, guided by iteration progress to balance reductions in the penalty function with improvements in constraint violation, while each penalty subproblem … Read more

    GFORS: GPU-Accelerated First-Order Method with Randomized Sampling for Binary Integer Programs

  • Ningji Wei
  • Jiaming Liang
    • Categories 0-1 Programming, Constrained Nonlinear Optimization, Parallel Algorithms Tags , ,

    We present GFORS, a GPU-accelerated framework for large binary integer programs. It couples a first-order (PDHG-style) routine that guides the search in the continuous relaxation with a randomized, feasibility-aware sampling module that generates batched binary candidates. Both components are designed to run end-to-end on GPUs with minimal CPU–GPU synchronization. The framework establishes near-stationary-point guarantees for … Read more

    A Simple First-Order Algorithm for Full-Rank Equality Constrained Optimization

  • Serge Gratton
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that reduce infeasibility, without using a merit function or a filter. The tangent steps are based on the AdaGrad method for unconstrained minimization. The … Read more

    A Simple Adaptive Proximal Gradient Method for Nonconvex Optimization

  • Ye Zilong
  • Shiqian Ma
  • Junfeng Yang
  • Danqing Zhou
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    Consider composite nonconvex optimization problems where the objective function consists of a smooth nonconvex term (with Lipschitz-continuous gradient) and a convex (possibly nonsmooth) term. Existing parameter-free methods for such problems often rely on complex multi-loop structures, require line searches, or depend on restrictive assumptions (e.g., bounded iterates). To address these limitations, we introduce a novel … Read more