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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…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
Linear programming (LP) is an extremely useful tool which 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…
This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low…
We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…
We introduce an efficient combination of polyhedral analysis and predicate partitioning. Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for…
Chain-of-Thought (CoT) has significantly enhanced the reasoning capabilities of Large Language Models (LLMs), especially when combined with reinforcement learning (RL) based post-training methods. While longer reasoning traces can improve…
Mathematical optimization is ubiquitous in modern applications. However, in practice, we often need to use nonlinear optimization models, for which the existing optimization tools such as Cplex or Gurobi may not be directly applicable and…
Solving mixed-integer optimization problems with embedded neural networks with ReLU activation functions is challenging. Big-M coefficients that arise in relaxing binary decisions related to these functions grow exponentially with the…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming least…
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 inverse problems we aim to reconstruct some underlying signal of interest from potentially corrupted and often ill-posed measurements. Classical optimization-based techniques proceed by optimizing a data consistency metric together with…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
We propose to generate Lagrangian cut for two-stage stochastic integer program by batch, in contrast to the existing methods which solve each Lagrangian subproblem at every iteration. We establish two convergence properties of the proposed…
We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…
Clustering is a fundamental tool that has garnered significant interest across a wide range of applications including text analysis. To improve clustering accuracy, many researchers have incorporated background knowledge, typically in the…
Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines learning methods on solver heuristics has shown potential to overcome this issue allowing for applications…