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A Parametric Approach for Solving Convex Quadratic Optimization with Indicators Over Trees

  • Aaresh Bhathena
  • Salar Fattahi
  • Andrés Gómez
  • Simge Küçükyavuz
    • Categories (Mixed) Integer Nonlinear Programming, Dynamic Programming, Quadratic Programming Tags , , , , ,

    This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive definite and its sparsity pattern corresponds to the adjacency matrix of a tree graph. We introduce a graph-based dynamic programming algorithm that solves this … Read more

    Learning-to-Optimize with PAC-Bayesian Guarantees: Theoretical Considerations and Practical Implementation

  • Michael Sucker
  • Jalal Fadili
  • Peter Ochs
    • Categories Optimization in Data Science, Other Topics Tags ,

    We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit trade-off between convergence guarantees and convergence speed, which contrasts with the typical worst-case analysis. Our learned optimization algorithms provably outperform related ones … Read more

    Horoballs and the subgradient method

  • Adrian Lewis
    • Categories Convex and Nonsmooth Optimization, Other Topics Tags , , , , ,

    To explore convex optimization on Hadamard spaces, we consider an iteration in the style of a subgradient algorithm. Traditionally, such methods assume that the underlying spaces are manifolds and that the objectives are geodesically convex: the methods are described using tangent spaces and exponential maps. By contrast, our iteration applies in a general Hadamard space, … Read more

    Preconditioned Barzilai-Borwein Methods for Multiobjective Optimization Problems

  • Jian Chen
    • Categories Multi-Criteria Optimization Tags , , ,

    Preconditioning is a powerful approach for solving ill-conditioned problems in optimization, where a preconditioning matrix is used to reduce the condition number and speed up the convergence of first-order method. Unfortunately, it is impossible to capture the curvature of all objective functions with a single preconditioning matrix in multiobjective optimization. Instead, second-order methods for multiobjective … Read more

    Second-Order Strong Optimality and Second-Order Duality for Nonsmooth Constrained Multiobjective Fractional Programming Problems

  • Chen Jiawei
  • Luyu Liu
  • Jen-Chih Yao
    • Categories Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , ,

    This paper investigates constrained nonsmooth multiobjective fractional programming problem (NMFP) in real Banach spaces. It derives a quotient calculus rule for computing the first- and second-order Clarke derivatives of fractional functions involving locally Lipschitz functions. A novel second-order Abadie-type regularity condition is presented, defined with the help of the Clarke directional derivative and the P´ales-Zeidan … Read more

    Fast convergence of the primal-dual dynamical system and algorithms for a nonsmooth bilinearly coupled saddle point problem

  • Kewei Ding
  • Jörg Fliege
  • Phan Vuong
    • Categories Game Theory, Nonsmooth Optimization Tags , , , ,

    This paper is devoted to study the convergence rates of a second-order dynamical system and its corresponding discretizations associated with a nonsmooth bilinearly coupled convex-concave saddle point problem. We derive the convergence rate of the primal-dual gap for the second-order dynamical system with asymptotically vanishing damping term. Based on the implicit discretization, we propose a … Read more

    On the Out-of-Sample Performance of Stochastic Dynamic Programming and Model Predictive Control

  • Dominic S. T. Keehan
  • Andrew B. Philpott
  • Edward Anderson
    • Categories Dynamic Programming, Stochastic Programming Tags , , ,

    Sample average approximation–based stochastic dynamic programming (SDP) and model predictive control (MPC) are two different methods for approaching multistage stochastic optimization. In this paper we investigate the conditions under which SDP may be outperformed by MPC. We show that, depending on the presence of concavity or convexity, MPC can be interpreted as solving a mean-constrained … Read more

    Black-box optimization for the design of a jet plate for impingement cooling

  • Filippo Marini
  • Margherita Porcelli
  • Elisa Riccietti
  • Lorenzo Cocchi
    • Categories Applications - Science and Engineering, Optimization of Simulated Systems, Other Topics Tags , , ,

    In this work, we propose a novel black-box formulation of the impingement cooling system for a nozzle in a gas turbine. Leveraging on a well-known model that correlates the design features of the cooling system with the efficiency parameters, we develop NOZZLE, a new constrained black-box optimization formulation for the jet impingement cooling design. Then … Read more

    A Jacobi-type Newton method for Nash equilibrium problems with descent guarantees

  • Oliver Kolossoski
  • Luís Felipe Bueno
  • Gabriel Haeser
    • Categories Game Theory, Nonlinear Optimization, Other Topics Tags , , , ,

    A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton’s method to the system obtained by the corresponding first-order necessary optimality conditions. However, when taking into account the game dynamics, it is not clear what is the goal of each player when considering they are taking their current … Read more

    Data Collaboration Analysis with Orthonormal Basis Selection and Alignment

  • Keiyu Nosaka
  • Yuichi Takano
  • Akiko Yoshise
    • Categories Linear, Cone and Semidefinite Programming, Optimization in Data Science, Other Topics

    Data Collaboration (DC) enables multiple parties to jointly train a model by sharing only linear projections of their private datasets. The core challenge in DC is to align the bases of these projections without revealing each party’s secret basis. While existing theory suggests that any target basis spanning the common subspace should suffice, in practice, … Read more