Month: June 2024

Efficient Low-rank Identification via Accelerated Iteratively Reweighted Nuclear Norm Minimization

  • Xiangyu Yang
  • Hao Wang
    • Categories Nonsmooth Optimization, Optimization in Data Science Tags , , , ,

    This paper considers the problem of minimizing the sum of a smooth function and the Schatten-\(p\) norm of the matrix. Our contribution involves proposing accelerated iteratively reweighted nuclear norm methods designed for solving the nonconvex low-rank minimization problem. Two major novelties characterize our approach. Firstly, the proposed method possesses a rank identification property, enabling the … Read more

    An Extended Validity Domain for Constraint Learning

  • Yilin Zhu
  • Samuel Burer
    • Categories Data Science Algorithms, Optimization in Data Science Tags , , , ,

    We consider embedding a predictive machine-learning model within a prescriptive optimization problem. In this setting, called constraint learning, we study the concept of a validity domain, i.e., a constraint added to the feasible set, which keeps the optimization close to the training data, thus helping to ensure that the computed optimal solution exhibits less prediction … Read more

    An novel adaptive inertial algorithm for solving bilevel variational inequalities with pseudomonotone multivalued operators

  • Zhongbao Wang
    • Categories Complementarity and Variational Inequalities

    This paper aims to develop an adaptive inertial algorithm for solving bilevel variational inequalities with multivalued pseudomonotone operators in real Hilbert spaces and establish its strong convergence property. The algorithm does not need to know the prior information of the Lipschitz constants and strong monotonicity coefficients of the associated mappings, incorporates inertial techniques and involves … Read more

    Stackelberg Games with k-Submodular Function under Distributional Risk-Receptiveness and Robustness

  • Seonghun Park
  • Manish Bansal
    • Categories Game Theory, Robust Optimization, Stochastic Programming

    We study submodular optimization in adversarial context, applicable to machine learning problems such as feature selection using data susceptible to uncertainties and attacks. We focus on Stackelberg games between an attacker (or interdictor) and a defender where the attacker aims to minimize the defender’s objective of maximizing a k-submodular function. We allow uncertainties arising from … Read more

    Exploiting Overlap Information in Chance-constrained Program with Random Right-hand Side

  • Wei Lv
  • Wei-Kun Chen
  • Yu-Hong Dai
  • Xiao-Jiao Tong
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    We consider the chance-constrained program (CCP) with random right-hand side under a finite discrete distribution. It is known that the standard mixed integer linear programming (MILP) reformulation of the CCP is generally difficult to solve by general-purpose solvers as the branch-and-cut search trees are enormously large, partly due to the weak linear programming relaxation. In … Read more

    Composite optimization models via proximal gradient method with a novel enhanced adaptive stepsize

  • Pham Thi Hoai
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    We first consider the convex composite optimization models with the local Lipschitzness condition imposed on the gradient of the differentiable term. The classical proximal gradient method will be studied with our novel enhanced adaptive stepsize selection. To obtain the convergence of the proposed algorithm, we establish a sufficient decrease type inequality associated with our new … Read more

    Robustness Analysis for Adaptive Optimization With Application to Industrial Decarbonization in the Netherlands

  • Justin Starreveld
  • Dick den Hertog
  • Jaron Davelaar
  • gregorbrandt
  • Nort Thijssen
    • Categories Applications - OR and Management Sciences, Energy, Robust Optimization Tags , , ,

    Robustness analysis assesses the performance of a particular solution under variation in the input data. This is distinct from sensitivity analysis, which assesses how variation in the input data changes a model’s optimal solution. For risk assessment purposes, robustness analysis has more practical value than sensitivity analysis. This is because sensitivity analysis, when applied to … Read more

    Stabilizing GNEP-Based Model Predictive Control: Quasi-GNEPs and End Constraints

  • Falk M. Hante
  • Martin Schmidt
  • Antonia Topalovic
    • Categories Other Topics Tags , , ,

    We present a feedback scheme for non-cooperative dynamic games and investigate its stabilizing properties. The dynamic games are modeled as generalized Nash equilibrium problems (GNEP), in which the shared constraint consists of linear time-discrete dynamic equations (e.g., sampled from a partial or ordinary differential equation), which are jointly controlled by the players’ actions. Further, the … Read more

    Optimization without Retraction on the Random Generalized Stiefel Manifold

  • Simon Vary
  • Bin Gao
  • Pierre-Antoine Absil
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , ,

    Optimization over the set of matrices \(X\) that satisfy \(X^\top B X = I_p\), referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as the canonical correlation analysis (CCA), independent component analysis (ICA), and the generalized eigenvalue problem (GEVP). Solving these problems is typically done by iterative methods … Read more

    Floorplanning with I/O assignment via feasibility-seeking and superiorization methods

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

    The feasibility-seeking approach offers a systematic framework for managing and resolving intricate constraints in continuous problems, making it a promising avenue to explore in the context of floorplanning problems with increasingly heterogeneous constraints. The classic legality constraints can be expressed as the union of convex sets. However, conventional projection-based algorithms for feasibility-seeking do not guarantee … Read more