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Generalized Nash equilibrium problems (GNEPs) arise in various applications where multiple players minimize individual cost functions subject to coupled constraints. A relatively unexplored approach to solving such problems is via a…

Semi-supervised semantic segmentation relieves the reliance on large-scale labeled data by leveraging unlabeled data. Recent semi-supervised semantic segmentation approaches mainly resort to pseudo-labeling methods to exploit unlabeled…

Designing high-performing metaheuristics for NP-hard combinatorial optimization problems, such as the Vehicle Routing Problem (VRP), remains a significant challenge, often requiring extensive domain expertise and manual tuning. Recent…

This paper studies the problem of graph-level clustering, which is a novel yet challenging task. This problem is critical in a variety of real-world applications such as protein clustering and genome analysis in bioinformatics. Recent years…

The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical…

Support vector machine is an important and fundamental technique in machine learning. In this paper, we apply a semismooth Newton method to solve two typical SVM models: the L2-loss SVC model and the \epsilon-L2-loss SVR model. The…

This study proposes a Newton based multiple objective optimization algorithm for hyperparameter search. The first order differential (gradient) is calculated using finite difference method and a gradient matrix with vectorization is formed…

Geometric programming is an important class of optimization problems that enable practitioners to model a large variety of real-world applications, mostly in the field of engineering design. In many real life optimization problem…

Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…

Optimal power flow (OPF) is an important problem in the operation of electric power systems. Due to the OPF problem's non-convexity, there may exist multiple local optima. Certifiably obtaining the global solution is important for certain…

We analyze a novel multi-level version of a recently introduced compressed sensing (CS) Petrov-Galerkin (PG) method from [H. Rauhut and Ch. Schwab: Compressive Sensing Petrov-Galerkin approximation of high-dimensional parametric operator…

Coordinate-wise minimization is a simple popular method for large-scale optimization. Unfortunately, for general (non-differentiable) convex problems it may not find global minima. We present a class of linear programs that coordinate-wise…

This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…

This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are…

We study semidefinite programming (SDP) relaxations for the NP-hard problem of globally optimizing a quadratic function over the Stiefel manifold. We introduce a strengthened relaxation based on two recent ideas in the literature: (i) a…

The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…

In the development of industrial digital twins, the optimization problem of technological and business processes often arises. In many cases, this problem can be reduced to a large-scale linear programming (LP) problem. The article is…

This paper concerns with the group zero-norm regularized least squares estimator which, in terms of the variational characterization of the zero-norm, can be obtained from a mathematical program with equilibrium constraints (MPEC). By…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…