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The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…

We devise a scheme for solving an iterative sequence of linear programs (LPs) or second order cone programs (SOCPs) to approximate the optimal value of any semidefinite program (SDP) or sum of squares (SOS) program. The first LP and…

A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational…

Inverse problems are ubiquitous in science and engineering. Many of these are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which…

Packing optimization is a prevalent problem that necessitates robust and efficient algorithms that are also simple to implement. One group of approaches is the raster methods, which rely on approximating the objects with pixelated…

We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient…

This paper develops a novel second order cone relaxation of the semidefinite programming formulation of optimal power flow, that does not imply the `angle relaxation'. We build on a technique developed by Kim et al., extend it for complex…

We address the problem of accelerating column generation (CG) for set-covering formulations via dual optimal inequalities (DOI). DOI use knowledge of the dual solution space to derive inequalities that might be violated by intermediate…

Many existing branch and bound algorithms for multiobjective optimization problems require a significant computational cost to approximate the entire Pareto optimal solution set. In this paper, we propose a new branch and bound algorithm…

Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…

In deep learning inference, model parameters are pruned and quantized to reduce the model size. Compression methods and common subexpression (CSE) elimination algorithms are applied on sparse constant matrices to deploy the models on…

Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…

Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known. The formulation counts sparse PCA with multiple…

In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. This problem minimizes a monotone ordered weighted median function of the distances between given demand points in $\mathbb{R}^d$ and its closest…

We study binary optimization problems of the form \( \min_{x\in\{-1,1\}^n} f(Ax-b) \) with possibly nonsmooth loss \(f\). Following the lifted rank-one semidefinite programming (SDP) approach\cite{qian2023matrix}, we develop a…

This paper is concerned with polynomial optimization problems. We show how to exploit term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of semidefinite programming relaxations. The novelty (and…

We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…

Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a…