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Complex engineering problems can be modelled as optimisation problems. For instance, optimising engines, materials, components, structure, aerodynamics, navigation, control, logistics, and planning is essential in aerospace. Metaheuristics…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…
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…
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…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
Function optimization and finding simultaneous solutions of a system of nonlinear equations (SNE) are two closely related and important optimization problems. However, unlike in the case of function optimization in which one is required to…
Large language models (LLMs) are increasingly used in learning algorithms, evaluations, and optimization tasks. Recent studies have shown that using LLM-based optimizers to automatically optimize model prompts, demonstrations, predictions…
Solutions to network optimization problems have greatly benefited from developments in nonlinear analysis, and, in particular, from developments in convex optimization. A key concept that has made convex and nonconvex analysis an important…
In many optimization problems in wireless communications, the expressions of objective function or constraints are hard or even impossible to derive, which makes the solutions difficult to find. In this paper, we propose a model-free…
Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data. However, the ultimate goal of learning is to minimize the error on future data (test error), for which the training…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
Optimization modeling plays a critical role in the application of Operations Research (OR) tools to address real-world problems, yet they pose challenges and require extensive expertise from OR experts. With the advent of large language…
Most decentralized optimization algorithms are handcrafted. While endowed with strong theoretical guarantees, these algorithms generally target a broad class of problems, thereby not being adaptive or customized to specific problem…
In the past 30 years, scientists have searched nature, including animals and insects, and biology in order to discover, understand, and model solutions for solving large-scale science challenges. The study of bionics reveals that how the…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical…
In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of…
Optimization algorithms and large language models (LLMs) enhance decision-making in dynamic environments by integrating artificial intelligence with traditional techniques. LLMs, with extensive domain knowledge, facilitate intelligent…
Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx=b, with an oracle providing evaluations of…