Fast convergence of inertial primal-dual dynamics and algorithms for a bilinearly coupled saddle point problem

  • Phan Vuong
    • Categories Convex Optimization Tags , , , , ,

    This paper is devoted to study the convergence rates of a second-order dynamical system and its corresponding discretization associated with a continuously differentiable bilinearly coupled convex-concave saddle point problem. First, we consider the second-order dynamical system with asymptotically vanishing damping term and show the existence and uniqueness of the trajectories as global twice continuously differentiable … Read more

    DeLuxing: Deep Lagrangian Underestimate Fixing for Column-Generation-Based Exact Methods

  • Yu Yang
    • Categories Branch and Cut Algorithms, Integer Programming, Transportation

    In this paper, we propose an innovative variable fixing strategy called deep Lagrangian underestimate fixing (DeLuxing). It is a highly effective approach for removing unnecessary variables in column-generation (CG)-based exact methods used to solve challenging discrete optimization problems commonly encountered in various industries, including vehicle routing problems (VRPs). DeLuxing employs a novel linear programming (LP) … Read more

    Affine FR : an effective facial reduction algorithm for semidefinite relaxations of combinatorial problems

  • Hao Hu
  • Boshi Yang
    • Categories 0-1 Programming, Convex Optimization, Semi-definite Programming

    We develop a new method called \emph{affine FR} for recovering Slater’s condition for semidefinite programming (SDP) relaxations of combinatorial optimization (CO) problems. Affine FR is a user-friendly method, as it is fully automatic and only requires a description of the problem. We provide a rigorous analysis of differences between affine FR and the existing methods. … Read more

    Using orthogonally structured positive bases for constructing positive k-spanning sets with cosine measure guarantees

  • Warren Hare
  • Clément W. Royer
  • Gabriel Jarry-Bolduc
  • Sébastien Kerleau
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , , ,

    Positive spanning sets span a given vector space by nonnegative linear combinations of their elements. These have attracted significant attention in recent years, owing to their extensive use in derivative-free optimization. In this setting, the quality of a positive spanning set is assessed through its cosine measure, a geometric quantity that expresses how well such … Read more

    A hybrid branch-and-bound and interior-point algorithm for stochastic mixed-integer nonlinear second-order cone programming

  • Baha Alzalg
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Second-Order Cone Programming Tags , , , ,

    One of the chief attractions of stochastic mixed-integer second-order cone programming is its diverse applications, especially in engineering (Alzalg and Alioui, {\em IEEE Access}, 10:3522-3547, 2022). The linear and nonlinear versions of this class of optimization problems are still unsolved yet. In this paper, we develop a hybrid optimization algorithm coupling branch-and-bound and primal-dual interior-point … Read more

    A Bilevel Optimization Approach for a Class of Combinatorial Problems with Disruptions and Probing

  • Leonardo Lozano
  • Juan Borrero
    • Categories Applications - OR and Management Sciences, Network Optimization, Stochastic Programming Tags , , ,

    We consider linear combinatorial optimization problems under uncertain disruptions that increase the cost coefficients of the objective function. A decision-maker, or planner, can invest resources to probe the components (i.e., the coefficients) in order to learn their disruption status. In the proposed probing optimization problem, the planner, knowing just the disruptions’ probabilities, selects which components … Read more

    Generalized asymmetric forward-backward-adjoint algorithms for convex-concave saddle-point problem

  • Jianchao Bai
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , ,

    The convex-concave minimax problem, also known as the saddle-point problem, has been extensively studied from various aspects including the algorithm design, convergence condition and complexity. In this paper, we propose a generalized asymmetric forward-backward-adjoint algorithm (G-AFBA) to solve such a problem by utilizing both the proximal techniques and the extrapolation of primal-dual updates. Besides applying … Read more

    Limited memory gradient methods for unconstrained optimization

  • Giulia Ferrandi
  • Michiel E. Hochstenbach
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , , ,

    The limited memory steepest descent method (Fletcher, 2012) for unconstrained optimization problems stores a few past gradients to compute multiple stepsizes at once. We review this method and propose new variants. For strictly convex quadratic objective functions, we study the numerical behavior of different techniques to compute new stepsizes. In particular, we introduce a method … Read more

    Adaptive Consensus: A network pruning approach for decentralized optimization

  • Suhail Mohmad Shah
  • Albert S. Berahas
  • Raghu Bollapragada
    • Categories Convex Optimization, Network Optimization, Nonlinear Optimization Tags , ,

    We consider network-based decentralized optimization problems, where each node in the network possesses a local function and the objective is to collectively attain a consensus solution that minimizes the sum of all the local functions. A major challenge in decentralized optimization is the reliance on communication which remains a considerable bottleneck in many applications. To … Read more