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Recently, we proposed a class of inequalities called lifted bilinear cover inequalities, which are second-order cone representable convex inequalities, and are valid for a set described by a separable bilinear constraint together with…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
An important challenge in multi-objective reinforcement learning is obtaining a Pareto front of policies to attain optimal performance under different preferences. We introduce Iterated Pareto Referent Optimisation (IPRO), which decomposes…
Multi-Objective Optimization (MOO) is an important problem in real-world applications. However, for a non-trivial problem, no single solution exists that can optimize all the objectives simultaneously. In a typical MOO problem, the goal is…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems,…
Multi-label classification (MLC) is an ML task of predictive modeling in which a data instance can simultaneously belong to multiple classes. MLC is increasingly gaining interest in different application domains such as text mining,…
Lead optimization in drug discovery requires efficiently navigating vast chemical space through iterative cycles to enhance molecular properties while preserving structural similarity to the original lead compound. Despite recent advances,…
Hyperspherical Prototypical Learning (HPL) is a supervised approach to representation learning that designs class prototypes on the unit hypersphere. The prototypes bias the representations to class separation in a scale invariant and known…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
We present several applications of the bias-variance decomposition, beginning with straightforward Monte Carlo estimation of integrals, but progressing to the more complex problem of Monte Carlo Optimization (MCO), which involves finding a…
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…
Learned optimizers (LOs) have the potential to significantly reduce the wall-clock training time of neural networks. However, they can struggle to optimize unseen tasks (meta-generalize), especially when training networks wider than those…
Large language models (LLMs) have significant potential to improve operational efficiency in operations management. Deploying these models requires specifying a policy that governs response quality, shapes user experience, and influences…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping…
Multimodal LLMs can accurately perceive numerical content across modalities yet fail to perform exact multi-digit multiplication when the identical underlying arithmetic problem is presented as numerals, number words, images, or in audio…