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Recently, machine learning, particularly message-passing graph neural networks (MPNNs), has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed up solving mixed-integer optimization problems by imitating…

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…

Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…

We present a novel efficient theoretical and numerical framework for solving global non-convex polynomial optimization problems. We analytically demonstrate that such problems can be efficiently reformulated using a non-linear objective…

Recent advances in Large Language Models (LLMs) have opened new perspectives for automation in optimization. While several studies have explored how LLMs can generate or solve optimization models, far less is understood about what these…

By virtue of its great utility in solving real-world problems, optimization modeling has been widely employed for optimal decision-making across various sectors, but it requires substantial expertise from operations research professionals.…

Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

Coordinate-wise minimization is a simple popular method for large-scale optimization. Unfortunately, for general (non-differentiable) convex problems it may not find global minima. We present a class of linear programs that coordinate-wise…

Evolutionary algorithms excel in solving complex optimization problems, especially those with multiple objectives. However, their stochastic nature can sometimes hinder rapid convergence to the global optima, particularly in scenarios…

Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by…

This paper presents AGGLIO (Accelerated Graduated Generalized LInear-model Optimization), a stage-wise, graduated optimization technique that offers global convergence guarantees for non-convex optimization problems whose objectives offer…

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…

We consider nonconvex optimization problem over simplex, and more generally, a product of simplices. We provide an algorithm, Langevin Multiplicative Weights Update (LMWU) for solving global optimization problems by adding a noise scaling…

Recent advances in LLM-guided evolutionary computation, particularly AlphaEvolve, have demonstrated remarkable success in discovering novel mathematical constructions and solving challenging optimization problems. In this article, we…

Multi-objective optimization problems (MOPs) are ubiquitous in real-world applications, presenting a complex challenge of balancing multiple conflicting objectives. Traditional evolutionary algorithms (EAs), though effective, often rely on…

Cooperative Co-evolution, through the decomposition of the problem space, is a primary approach for solving large-scale global optimization problems. Typically, when the subspaces are disjoint, the algorithms demonstrate significantly both…

Large language models (LLMs) have demonstrated exceptional performance not only in natural language processing tasks but also in a great variety of non-linguistic domains. In diverse optimization scenarios, there is also a rising trend of…