Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 34 for “"Nonconvex Optimization"”.
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ON RICCATI EQUATIONS IN NONCONVEX OPTIMIZATION
Convex optimization serves as a foundational pillar for modern engineering and data science, providing highly efficient algorithms that reliably converge to a global optimal solution across diverse modeling applications. However many problems in engineering and data-science fall outside of the …
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Cutting Planes for Convex Objective Nonconvex Optimization
… studies methods for tightening relaxations of optimization problems with convex objective values over a nonconvex domain. A class of linear inequalities obtained by lifting easily obtained valid inequalities is introduced, and it is shown that this class of inequalities is sufficient to …
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Bayesian coresets: Revisiting the nonconvex optimization perspective
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms
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Analysis of critical points for nonconvex optimization
… establish sufficient conditions under which an optimization problem has a unique local optimum. Motivated by the practical need for establishing the uniqueness of the optimum in an optimization problem in fields such as global optimization, equilibrium analysis, and efficient algorithm design, …
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Exploitable structures and complexities of modern nonconvex optimization: Fundamental limits and efficient algorithms
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-08-01
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Discrete and Continuous Nonconvex Optimization: Decision Trees, Valid Inequalities, and Reduced Basis Techniques
… management problem via a novel decision tree optimization approach, as well as development of enhanced Reformulation-Linearization Technique (RLT)-based linear programming (LP) relaxations for solving nonconvex polynomial programming problems, through the generation of valid inequalities and …
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Nonconvex optimization algorithm with a new Bi-criteria selection of potential simplices using an estimate of Lipschitz constant /
… which are often applied for practical black-box optimization problems, are considered. The main goal of this thesis is set - to propose a global optimization algorithm for Lipschitz functions with unknown Lipschitz constants in order to efficiently spend potentially expensive function …
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Semidefinite Cuts and Partial Convexification Techniques with Applications to Continuous Nonconvex Optimization, Stochastic Integer Programming, and Facility Layout Problems
… general and problem-specific applications within nonconvex optimization, exploiting the constructs of the Reformulation-Linearization Technique (RLT). We begin by developing a technique to enhance general problems in nonconvex optimization through the use of a new class of RLT cuts, called …
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Advances in Nonconvex and Robust Optimization
Nonconvex optimization presents significant challenges, as identifying the global optimum is often difficult. This thesis introduces novel algorithms to find the exact solution of a broad class of nonconvex optimization problems. The thesis is structured into four parts. In Chapter 2, we propose a …
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Robust Nonlinear Control Using Bilinear Matrix Inequalities With Application to a Batch Crystallization Process
… design problem necessitates the solution of an optimization problem under bilinear matrix inequality constraints, which is a nonconvex optimization problem, has been shown to be NP-hard, and its efficient solution is also an open research problem. Various solution strategies have been …
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The Sum-Product Theorem and its Applications
… for many problems in AI and ML, including nonconvex optimization, computer vision, and deep learning. I first identify and prove the sum-product theorem, which states that in any semiring for inference to be tractable it suffices that the factors of every product have disjoint scopes; i.e., …
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Solving Factorable Programs with Applications to Cluster Analysis, Risk Management, and Control Systems Design
… in many diverse fields. The field of discrete optimization came to the forefront as a result of the impressive developments in the area of linear programming. Although discrete optimization problems can be viewed as belonging to the class of nonconvex programs, it has only been in recent times …
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Traversing Rugged Domains: Explorations in Non-convex Optimization Theory and Software
… and computational frameworks for nonlinear, nonconvex optimization problems in statistics, machine learning, and optimal control. Disciplined Geodesically Convex Programming (DGCP) extends convexity verification to Riemannian manifolds, enabling optimization on curved spaces with global …
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Optimisation models and algorithms for multicast message routing and power control in wireless multihop networks
… can therefore be represented as a nonlinear optimization problem over network flow variables and communication resource variables. In this thesis we develop a nonconvex optimization problem for transmitting unicast and multicast messages through a time-slotted multi-hop wireless network. …
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Accelerated algorithms for constrained optimization and control
Nonlinear optimization with equality and inequality constraints is a ubiquitous problem in several optimization and control problems in large-scale systems. Ensuring feasibility along with reasonable convergence to optimal solution remains an open and pressing problem in this area. A class of …
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Convexification and Global Optimization of Problems Involving the Euclidean Norm
The field of deterministic global optimization has advanced significantly over the last several decades, enabled by the development of new algorithmic techniques and improved computer hardware, and is experiencing a surge of interest. However, global optimization methods for general nonlinear …
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Strategic algorithms
… both mean and standard deviation, we run into nonconvex optimization challenges that require new theory beyond classical shortest path algorithm design. Yet another shortest path application, routing of packets in the Internet, needs to further incorporate economic incentives to reflect the …
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Quantum Advantage via Physics-Inspired Methods in Optimization: Empirical and Theoretical Analysis
Continuous and combinatorial optimization are foundational to science and engineering. While convex optimization can be usually tackled efficiently, large-scale nonconvex optimization and combinatorial optimization remain a significant challenge for classical computation.Physics-inspired quantum …
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Mixed-integer convex optimization : outer approximation algorithms and modeling power
In this thesis, we study mixed-integer convex optimization, or mixed-integer convex programming (MICP), the class of optimization problems where one seeks to minimize a convex objective function subject to convex constraints and integrality restrictions on a subset of the variables. We focus on two …
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Design of Low-Order Controllers using Optimization Techniques
… been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers. The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods …
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