T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization

  • Hiroki Marumo
  • Sunyoung Kim
  • Makoto Yamashita
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , , ,

    We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs was introduced by Zheng, Huang and Hu in 2022. In this work, we propose a T-SDP relaxation for POPs with polynomial inequality constraints and show that the resulting T-SDP relaxation formulated with third-order tensors can be transformed into … Read more

    Riemannian trust-region methods for strict saddle functions with complexity guarantees

  • Florentin Goyens
  • Clément W. Royer
    • Categories Nonlinear Optimization Tags , , ,

    The difficulty of minimizing a nonconvex function is in part explained by the presence of saddle points. This slows down optimization algorithms and impacts worst-case complexity guarantees. However, many nonconvex problems of interest possess a favorable structure for optimization, in the sense that saddle points can be escaped efficiently by appropriate algorithms. This strict saddle … Read more

    Extending the Reach of First-Order Algorithms for Nonconvex Min-Max Problems with Cohypomonotonicity

  • Ahmet Alacaoglu
  • Donghwan Kim
  • Stephen Wright
    • Categories Complementarity and Variational Inequalities, Generalized Convexity/Monoticity, Nonlinear Optimization, Stochastic Programming

    \(\) We focus on constrained, \(L\)-smooth, nonconvex-nonconcave min-max problems either satisfying \(\rho\)-cohypomonotonicity or admitting a solution to the \(\rho\)-weakly Minty Variational Inequality (MVI), where larger values of the parameter \(\rho>0\) correspond to a greater degree of nonconvexity. These problem classes include examples in two player reinforcement learning, interaction dominant min-max problems, and certain synthetic test problems … 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

    Accurate and Warm-Startable Linear Cutting-Plane Relaxations for ACOPF

  • Daniel Bienstock
  • Matias Villagra
    • Categories Convex Optimization, Energy, Linear, Cone and Semidefinite Programming Tags , ,

    We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone relaxations for ACOPF along with modern cut management techniques. These techniques prove effective on a broad family of ACOPF instances, including the largest … Read more

    Strategic Planning in Citriculture: An Optimization Approach

  • Cassiano Tavares
  • Pedro Munari
    • Categories Applications - OR and Management Sciences

    The worldwide citrus market has been impacted by various factors in recent years, including population growth, phytosanitary diseases, high costs of agricultural inputs, and diminishing planting areas. As a consequence, producers in this sector have attempted to find tools to support strategic planting decisions, and thus meet international contract demands. This paper proposes an optimization … Read more

    Cuts and semidefinite liftings for the complex cut polytope

  • Lennart Sinjorgo
  • Renata Sotirov
  • Miguel F. Anjos
    • Categories Polyhedra, Semi-definite Programming, Telecommunications Tags , , , , ,

    \(\) We consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices \(xx^{\mathrm{H}}\), where the elements of \(x \in \mathbb{C}^n\) are \(m\)th unit roots. These polytopes have applications in \({\text{MAX-3-CUT}}\), digital communication technology, angular synchronization and more generally, complex quadratic programming. For \({m=2}\), the complex cut polytope corresponds to the well-known cut … Read more

    Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

  • Robert Baraldi
  • Stefan M. Wild
  • Sven Leyffer
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , ,

    Nonconvex, nonlinear cost functions arise naturally in physical inverse problems and machine learning. The alternating direction method of multipliers (ADMM) has seen extensive use in these applications, despite exhibiting uncertain convergence behavior in many practical nonconvex settings, and struggling with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential … Read more

    Riemannian Bilevel Optimization

  • Jiaxiang Li
  • Shiqian Ma
    • Categories Nonlinear Optimization Tags ,

    In this work, we consider the bilevel optimization problem on Riemannian manifolds. We inspect the calculation of the hypergradient of such problems on general manifolds and thus enable the utilization of gradient-based algorithms to solve such problems. The calculation of the hypergradient requires utilizing the notion of Riemannian cross-derivative and we inspect the properties and … Read more

    Store Fulfillment with Autonomous Mobile Robots and In-Store Customers

  • Joyjit Bhowmick
  • Jennifer Pazour
  • Iman Dayarian
    • Categories Production and Logistics, Supply Chain Management, Transportation

    Omnichannel services, such as buy-online-pickup-in-store, curbside pickup, and ship-from-store, have shifted the order-picking tasks previously completed by in-store customers doing their own shopping to the retailer’s responsibility. To fulfill these orders, many retailers have deployed a store fulfillment strategy, where online orders are picked from brick-and-mortar retail store shelves. We focus on the design of … Read more