Nonlinear Optimization

A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems

  • Qi Wang
  • Frank E. Curtis
  • Daniel P. Robinson
  • Vyacheslav Kungurtsev
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science Tags , ,

    A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results. The algorithm is unique from other interior-point methods for solving smooth (nonconvex) optimization problems since the search directions are computed using stochastic gradient estimates. It is also unique … Read more

    A New Inexact Proximal Linear Algorithm with Adaptive Stopping Criteria for Robust Phase Retrieval

  • Zhong Zheng
  • Shiqian Ma
  • Lingzhou Xue
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions are two adaptive stopping criteria for the subproblem. The convergence behavior of the proposed methods is analyzed. Through experiments on … Read more

    A minimal face constant rank constraint qualification for reducible conic programming

  • Roberto Andreani
  • Gabriel Haeser
  • leomakoto
  • Héctor Ramírez
    • Categories Cone Programming, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , ,

    \(\) In a previous paper [R. Andreani, G. Haeser, L. M. Mito, H. Ramírez, T. P. Silveira. First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition. Mathematical Programming, 2023. DOI: 10.1007/s10107-023-01942-8] we introduced a constant rank constraint qualification for nonlinear semidefinite and second-order cone programming by considering all … Read more

    A descent method for nonsmooth multiobjective optimization problems on Riemannian manifolds

  • Chunming Tang
  • Hao He
  • Jinbao Jian
  • Miantao Chao
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags

    In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in existing methods. A necessary condition for Pareto optimality in Euclidean space is generalized to the Riemannian setting. At every iteration, an acceptable … Read more

    Per-RMAP: Feasibility-Seeking and Superiorization Methods for Floorplanning with I/O Assignment

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

    The feasibility-seeking approach provides a systematic scheme to manage and solve complex constraints for continuous problems, and we explore it for the floorplanning problems with increasingly heterogeneous constraints. The classic legality constraints can be formulated as the union of convex sets. However, the convergence of conventional projection-based algorithms is not guaranteed when the constraints sets … Read more

    Heuristic methods for noisy derivative-free bound-constrained mixed-integer optimization

  • Morteza Kimiaei
  • Arnold Neumaier
    • Categories (Mixed) Integer Nonlinear Programming, Bound-constrained Optimization, Global Optimization Tags

    This paper discusses MATRS, a new matrix adaptation trust region strategy for solving noisy derivative-free mixed-integer optimization problems with simple bounds.  MATRS repeatedly cycles through five phases, mutation, selection, recombination, trust-region, and mixed-integer in this order. But if in the mutation phase a new best point (point with lowest inexact function value among all evaluated … Read more

    The alternating simultaneous Halpern-Lions-Wittmann-Bauschke algorithm for finding the best approximation pair for two disjoint intersections of convex sets

  • Yair Censor
  • Rafiq Mansour
  • Daniel Reem
    • Categories Approximation Algorithms, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , ,

    Given two nonempty and disjoint intersections of closed and convex subsets, we look for a best approximation pair relative to them, i.e., a pair of points, one in each intersection, attaining the minimum distance between the disjoint intersections. We propose an iterative process based on projections onto the subsets which generate the intersections. The process … Read more

    Non-asymptotic superlinear convergence of Nesterov accelerated BFGS

  • Manish Kumar Sahu
  • Suvendu Pattanaik
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    This paper studies the convergence of a Nesterov accelerated variant of the Broyden-Fletcher-Goldfarb-Shanno (NA-BFGS) quasi-Newton method in the setting where the objective function is strongly convex, its gradient is Lipschitz continuous, and its Hessian is Lipschitz continuous at the optimal point. We demonstrate that similar to the classic BFGS method, the Nesterov accelerated BFGS method … Read more

    Hidden convexity, optimization, and algorithms on rotation matrices

  • Kevin Shu
  • Alex L. Wang
  • Akshay Ramachandran
    • Categories Constrained Nonlinear Optimization, Other Topics, Semi-definite Programming Tags , ,

    \(\) This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices \(\text{SO}(n)\). Such problems are nonconvex due to the constraint\(X\in\text{SO}(n)\). Nonetheless, we show that certain linear images of \(\text{SO}(n)\) are convex, opening up the possibility for convex optimization algorithms with provable guarantees for these problems. Our main technical … Read more

    An active set method for bound-constrained optimization

  • Arnold Neumaier
  • Behzad Azmi
  • Morteza Kimiaei
    • Categories Bound-constrained Optimization, Nonlinear Optimization Tags

    In this paper, a class of algorithms is developed for bound-constrained optimization. The new scheme uses the gradient-free line search along bent search paths. Unlike traditional algorithms for bound-constrained optimization, our algorithm ensures that the reduced gradient becomes arbitrarily small. It is also proved that all strongly active variables are found and fixed after finitely … Read more