Related papers: Computing Binary Integer Programming via A New Exa…
In recent years, several integer programming (IP) approaches were developed for maximum-likelihood decoding and minimum distance computation for binary linear codes. Two aspects in particular have been demonstrated to improve the…
We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying…
We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. We prove convergence of our numerical method under reasonably mild assumptions: boundedness and…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
In this paper, we investigate a class of non-convex sum-of-ratios programs relevant to decision-making in key areas such as product assortment and pricing, and facility location and cost planning. These optimization problems, characterized…
Binary segmentation, which is sequential in nature is thus far the most widely used method for identifying multiple change points in statistical models. Here we propose a top down methodology called arbitrary segmentation that proceeds in a…
We develop a general equality-constrained nonlinear optimization algorithm based on a smooth penalty function proposed by Fletcher (1970). Although it was historically considered to be computationally prohibitive in practice, we demonstrate…
We propose an exact algorithm for solving biobjective integer programming problems, which arise in various applications of operations research. The algorithm is based on solving Pascoletti-Serafini scalarizations to search specified regions…
This paper proposes a Heaviside composite optimization approach and presents a progressive (mixed) integer programming (PIP) method for solving multi-class classification and multi-action treatment problems with constraints. A Heaviside…
In this work, we introduce and study the $p$-$\alpha$-closest-center problem ($p\alpha$CCP), which generalizes the $p$-second-center problem, a recently emerged variant of the classical $p$-center problem. In the $p\alpha$CCP, we are given…
This paper presents a new hybrid classical-quantum approach to solve Mixed Integer Linear Programming (MILP) using neutral atom quantum computations. We apply Benders decomposition (BD) to segment MILPs into a master problem (MP) and a…
We propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems. A rapidly convergent fixed point method is developed for a regularized penalty functional. The applicability…
Physics-informed extreme learning machines (PIELMs) typically impose boundary and initial conditions through penalty terms, yielding only approximate satisfaction that is sensitive to user-specified weights and can propagate errors into the…
Bregman proximal point algorithm (BPPA) has witnessed emerging machine learning applications, yet its theoretical understanding has been largely unexplored. We study the computational properties of BPPA through learning linear classifiers…
We consider the 0-1 Penalized Knapsack Problem (PKP). Each item has a profit, a weight and a penalty and the goal is to maximize the sum of the profits minus the greatest penalty value of the items included in a solution. We propose an…
We present a semi-infinite program (SIP) solver for trajectory optimizations of general articulated robots. These problems are more challenging than standard Nonlinear Program (NLP) by involving an infinite number of non-convex, collision…
Multi-armed bandit (MAB) is a class of online learning problems where a learning agent aims to maximize its expected cumulative reward while repeatedly selecting to pull arms with unknown reward distributions. We consider a scenario where…
We study a general convex optimization problem, which covers various classic problems in different areas and particularly includes many optimal transport related problems arising in recent years. To solve this problem, we revisit the…