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 142 for “"nonconvex"”.
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Nonconvex robust optimization
… optimization technique, which is applicable to nonconvex and simulation-based problems. Robust optimization finds decisions with the best worst-case performance under uncertainty. If constraints are present, decisions should also be feasible under perturbations. In the real-world, many problems …
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SPARSE RECOVERY BY NONCONVEX LIPSHITZIAN MAPPINGS
… on fixed-point iteration scheme which combines nonconvex Lipschitzian-type mappings with canonical orthogonal projectors. The first are aimed at uniformly enhancing the sparseness level by shrinking effects, the latter to project back into the feasible space of solutions. In the second part of …
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ON RICCATI EQUATIONS IN NONCONVEX OPTIMIZATION
… or methods lacking worst-case guarantees. Nonconvexity does not always invalidate the intuition and methods developed for convex problems, especially when especially when some of the structures leading to convexity remain intact. It is often possible to preserve feasibility through …
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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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Cutting Planes for Convex Objective Nonconvex 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 describe the epigraph of a convex and differentiable function …
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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
In this thesis, we 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 …
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Stochastic Homogenization of Nonconvex Hamilton-Jacobi Equations in One Dimension
… essential behavior of the system. We consider nonconvex Hamilton-Jacobi equations in one space dimension. We provide a fully constructive proof of homogenization, which yields a formula for the effective Hamiltonian. Our proof employs sublinear correctors, functions extensively discussed in the …
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Guiding Nonconvex Trajectory Optimization with Hierarchical Graphs of Convex Sets
… with trajectory optimization is inherently nonconvex. Some of this nonconvexity is fundamental: the robot might need to make a discrete decision to go left around an obstacle or right around an obstacle. Some of this nonconvexity is potentially more benign: we might want to penalize …
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Semidefinite relaxation based branch-and-bound method for nonconvex quadratic programming
… based branch-and-bound method to solve nonconvex quadratic programming problems. Firstly, we show an interval branch-and-bound method to calculate the bounds for the minimum of bounded polynomials. Then we demonstrate four SDP relaxation methods to solve nonconvex Box constrained …
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Global Optimization of Nonconvex Factorable Programs with Applications to Engineering Design Problems
… optimization algorithm to solve a class of nonconvex programming problems, and to test it using a collection of engineering design problem applications.The class of problems we consider involves the optimization of a general nonconvex factorable objective function over a feasible region that …
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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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Global Optimization of the Nonconvex Containership Design Problem Using the Reformulation-Linearization Technique
… design problem involves optimizing a nonconvex objective function over a design space that is restricted by a set of constraints defined in terms of nonconvex functions. An application of standard nonlinear optimization methods to such a problem can at best attain a local optimum that …
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Discrete and Continuous Nonconvex Optimization: Decision Trees, Valid Inequalities, and Reduced Basis Techniques
… linear programming (LP) relaxations for solving nonconvex polynomial programming problems, through the generation of valid inequalities and reduced representations, along with the design and implementation of efficient algorithms. We first conduct a quantitative analysis for a strategic risk …
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On the Complexity of Nonconvex-Strongly-Concave Smooth Minimax Optimization Using First-Order Methods
… the full picture is known. However, the general nonconvex-concave setting is less understood. In this work, we study the complexity of nonconvex-strongly-concave minimax optimization using first-order methods. First, we provide a first-order oracle complexity lower bound for finding stationary …
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Nonconvex optimization algorithm with a new Bi-criteria selection of potential simplices using an estimate of Lipschitz constant /
In this thesis, Direct (DIviding RECTangles) type algorithms based on Lipschitz objective function models with unknown 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 …
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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 Computer-Assisted Design and Analysis of First-Order Optimization Methods and Related Problems
… and designing first-order methods using nonconvex quadratically constrained quadratic optimization problems (QCQPs). In this approach, the key idea involves posing the analysis or design of first-order methods as nonconvex but practically tractable QCQPs and then solving them to global …
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Solving Factorable Programs with Applications to Cluster Analysis, Risk Management, and Control Systems Design
… can be viewed as belonging to the class of nonconvex programs, it has only been in recent times that optimization research has confronted the more formidable class of continuous nonconvex optimization problems, where the objective function and constraints are often highly nonlinear and …
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The extreme point mathematical programming problem
This dissertation deals with a class of nonconvex mathematical programs called Extreme Point Mathematical Programs (EPMP). These problems are generalizations of certain Integer Programming problems and also find their application in other nonconvex programs like the Concave Minimization problem. …
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