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Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning…

Often times, in many design problems, there is a need to select a small set of informative or representative elements from a large ground set of entities in an optimal fashion. Submodular optimization that provides for a formal way to solve…

Shooting methods are an efficient approach to solving nonlinear optimal control problems. As they use local optimization, they exhibit favorable convergence when initialized with a good warm-start but may not converge at all if provided…

Multi-task learning is a very challenging problem in reinforcement learning. While training multiple tasks jointly allow the policies to share parameters across different tasks, the optimization problem becomes non-trivial: It remains…

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for…

With the rapid development of large language models (LLMs) and the growing demand for personalized content, recommendation systems have become critical in enhancing user experience and driving engagement. Collaborative filtering algorithms,…

A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…

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…

We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of…

We propose a multi-swarm approach to approximate the Pareto front of general multi-objective optimization problems that is based on the Consensus-based Optimization method (CBO). The algorithm is motivated step by step beginning with a…

In this short note, we discuss a goal-oriented multiobjective optimization problem for system performance assessment. The objective function for such optimization problem, which is usually a composite of different performance indices…

In this paper, we remark on the published paper "Treatment of Set-Valued Robustness via Separation and Scalarization" [1], which deals with the robust solution to an uncertain constrained set-valued optimization problem via scalarization…

The superiorization methodology (SM) is an optimization heuristic in which an iterative algorithm, which aims to solve a particular problem, is ``superiorized'' to promote solutions that are improved with respect to some secondary…

In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering…

Quantization can be used to form new vectors/matrices with shared values close to the original. In recent years, the popularity of scalar quantization for value-sharing applications has been soaring as it has been found huge utilities in…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…

Gradient-based optimization has been critical to the success of machine learning, updating a single set of parameters to minimize a single loss. A growing number of applications rely on a generalization of this, where we have a bilevel or…

Bayesian optimization (BO) is a model-based approach for gradient-free black-box function optimization. Typically, BO is powered by a Gaussian process (GP), whose algorithmic complexity is cubic in the number of evaluations. Hence, GP-based…

This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks…