相关论文: On Partial Opimality by Auxiliary Submodular Probl…

Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…

We consider the class of polynomial optimization problems $\inf \{f(x):x\in K\}$ for which the quadratic module generated by the polynomials that define $K$ and the polynomial $c-f$ (for some scalar $c$) is Archimedean. For such problems,…

We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…

Initially developed for the min-knapsack problem, the knapsack cover inequalities are used in the current best relaxations for numerous combinatorial optimization problems of covering type. In spite of their widespread use, these…

We consider the MAP-inference problem for graphical models, which is a valued constraint satisfaction problem defined on real numbers with a natural summation operation. We propose a family of relaxations (different from the famous…

In this contribution, we are concerned with parameter optimization problems that are constrained by multiscale PDE state equations. As an efficient numerical solution approach for such problems, we introduce and analyze a new relaxed and…

Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…

In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and computational properties of this relaxation. As evident from our…

The optimization problems with simple bounds are an important class of problems. To facilitate the computation of such problems, an unconstrained-like dynamic method, motivated by the Lyapunov control principle, is proposed. This method…

This paper introduces a novel approach to evaluating the asymptotic stability of equilibrium points in both continuous-time (CT) and discrete-time (DT) nonlinear autonomous systems. By utilizing indirect Lyapunov methods and linearizing…

Ising machines (IM) are physics-inspired alternatives to von Neumann architectures for solving hard optimization tasks. By mapping binary variables to coupled Ising spins, IMs can naturally solve unconstrained combinatorial optimization…

We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…

We investigate the maximum happy vertices (MHV) problem and its complement, the minimum unhappy vertices (MUHV) problem. We first show that the MHV and MUHV problems are a special case of the supermodular and submodular multi-labeling…

We give a simple deterministic $O(\log K / \log\log K)$ approximation algorithm for the Min-Max Selecting Items problem, where $K$ is the number of scenarios. While our main goal is simplicity, this result also improves over the previous…

This paper is devoted to developing the alternating minimization algorithm for problems of structured nonconvex optimization proposed by Attouch, Bolt\'e, Redont, and Soubeyran in 2010. Our main result provides significant improvements of…

Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…

In this paper, we extend two classes of functions involved in asymptotic stability analyses. The goal of this extension is to study a maximization problem on the reachable values of a discrete-time dynamical system. This specific…

This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…

The semidefinite programming (SDP) relaxation has proven to be extremely strong for many hard discrete optimization problems. This is in particular true for the quadratic assignment problem (QAP), arguably one of the hardest NP-hard…

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…