Related papers: Differentiable Extensions with Rounding Guarantees…
In the submodular cover problem, we are given a non-negative monotone submodular function $f$ over a ground set $E$ of items, and the goal is to choose a smallest subset $S \subseteq E$ such that $f(S) = Q$ where $Q = f(E)$. In the…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
Many hard problems in the computational sciences are equivalent to counting the leaves of a decision tree, or, more generally, summing a cost function over the nodes. These problems include calculating the permanent of a matrix, finding the…
Two prominent challenges in explainability research involve 1) the nuanced evaluation of explanations and 2) the modeling of missing information through baseline representations. The existing literature introduces diverse evaluation…
Any square matrix can be transformed into a doubly stochastic matrix via Sinkhorn scaling with diagonal matrices or completing to a larger dimensional matrix. Standard Birkhoff-von Neumann and Pauli decompositions represent such matrices as…
The numerical optimization of continuous functions is a fundamental task in many scientific and engineering domains, ranging from mechanical design to training of artificial intelligence models. Among the most effective and widely used…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
We introduce new diversification methods for zero-one optimization that significantly extend strategies previously introduced in the setting of metaheuristic search. Our methods incorporate easily implemented strategies for partitioning…
We propose a general analytical framework for single-facility continuous location problems under spatial demand uncertainty. In contrast to classical formulations based on discrete or regionally aggregated demands, the proposed model…
Optimization over the set of matrices $X$ that satisfy $X^\top B X = I_p$, referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as the canonical correlation analysis (CCA),…
Bayesian optimization (BO) is a sample efficient approach to automatically tune the hyperparameters of machine learning models. In practice, one frequently has to solve similar hyperparameter tuning problems sequentially. For example, one…
This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem…
Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
We introduce a novel alignment method for diffusion models from distribution optimization perspectives while providing rigorous convergence guarantees. We first formulate the problem as a generic regularized loss minimization over…
Differential Evolution (DE) is a renowned optimization stratagem that can easily solve nonlinear and comprehensive problems. DE is a well known and uncomplicated population based probabilistic approach for comprehensive optimization. It has…
Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…
Multi-objective optimization problems are ubiquitous in real-world science, engineering and design optimization problems. It is not uncommon that the objective functions are as a black box, the evaluation of which usually involve…
Decentralized optimization provides a fundamental framework for large-scale learning and signal processing with distributed data. We study decentralized optimization with orthogonality constraints on the Stiefel manifold and propose…