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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 without exposing their private datasets. Each party privately transforms its data using a secret linear basis and shares only the resulting intermediate representations. Existing theory asserts that any target basis spanning the same subspace as the secret bases should suffice; however, empirical evidence reveals … Read more

    Uncertainty Quantification for Multiobjective Stochastic Convex Quadratic Programs

  • Ziyu Liu
  • Susan R. Hunter
  • Nan Kong
  • Raghu Pasupathy
    • Categories Multi-Criteria Optimization, Quadratic Programming, Stochastic Programming

    A multiobjective stochastic convex quadratic program (MOSCQP) is a multiobjective optimization problem with convex quadratic objectives that are observed with stochastic error. MOSCQP is a useful problem formulation arising, for example, in model calibration and nonlinear system identification when a single regression model combines data from multiple distinct sources, resulting in a multiobjective least squares … Read more

    On Coupling Constraints in Linear Bilevel Optimization

  • Dorothee Henke
  • Henri Lefebvre
  • Martin Schmidt
  • Johannes Thürauf
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities, Other Topics Tags ,

    It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and without coupling constraints w.r.t. their complexity-theoretical hardness. In this note, we prove that, although there is a clear difference between these … Read more

    Solution methods for partial inverse combinatorial optimization problems in which weights can only be increased

  • Eva Ley
  • Maximilian Merkert
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Game Theory Tags , , ,

    Partial inverse combinatorial optimization problems are bilevel optimization problems in which the leader aims to incentivize the follower to include a given set of elements in the solution of their combinatorial problem. If the set of required elements defines a complete follower solution, the inverse combinatorial problem is solvable in polynomial time as soon as … Read more

    Policy with guaranteed risk-adjusted performance for multistage stochastic linear problems

  • Bernardo Freitas Paulo da Costa
  • Vincent Leclère
    • Categories Convex Optimization, Dynamic Programming, Stochastic Programming Tags , , ,

    Risk-averse multi-stage problems and their applications are gaining interest in various fields of applications. Under convexity assumptions, the resolution of these problems can be done with trajectory following dynamic programming algorithms like Stochastic Dual Dynamic Programming (SDDP) to access a deterministic lower bound, and dual SDDP for deterministic upper bounds. In this paper, we leverage … Read more