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We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When…
This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem…
We propose a complete quantum-classical hybrid branch-and-bound algorithm (QCBB) to solve binary linear programs with equality constraints. That includes bound calculation, convergence metrics and optimality guarantee to the quantum…
In this paper, we describe a new scalable and modular material point method (MPM) code developed for solving large-scale problems in continuum mechanics. The MPM is a hybrid Eulerian-Lagrangian approach, which uses both moving material…
Block majorization-minimization (BMM) is a simple iterative algorithm for constrained nonconvex optimization that sequentially minimizes majorizing surrogates of the objective function in each block while the others are held fixed. BMM…
We introduce a new method for robust beamforming, where the goal is to estimate a signal from array samples when there is uncertainty in the angle of arrival. Our method offers state-of-the-art performance on narrowband signals and is…
In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is…
In bipartite matching problems, vertices on one side of a bipartite graph are paired with those on the other. In its online variant, one side of the graph is available offline, while the vertices on the other side arrive online. When a…
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions…
Many problems arising in image processing and signal recovery with multi-regularization can be formulated as minimization of a sum of three convex separable functions. Typically, the objective function involves a smooth function with…
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…
The success of large language models has garnered widespread attention for model merging techniques, especially training-free methods which combine model capabilities within the parameter space. However, two challenges remain: (1) uniform…
In this paper, we consider nonconvex optimization problems with nonsmooth nonconvex objective function and nonlinear equality constraints. We assume that both the objective function and the functional constraints can be separated into 2…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the…
In many real-world applications, data are represented by matrices or high-order tensors. Despite the promising performance, the existing two-dimensional discriminant analysis algorithms employ a single projection model to exploit the…
We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…
We consider the minimum-norm-point (MNP) problem over polyhedra, a well-studied problem that encompasses linear programming. We present a general algorithmic framework that combines two fundamental approaches for this problem: active set…