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 22 for “"Positive semidefinite"”.
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Voltooiingsprobleme vir klasse van reële simmetriese matrikse wat geslote konvekse keëls vorm
… problem of the SPN matrix, which is the sum of a positive semidefinite matrix and a nonnegative matrix, forms the main focus of this study. The completion problems of positive semidefinite matrices, completely positive matrices and SPN matrices are directly related to a certain graph that …
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On a graph parameter related to vertex labelings and its application to minimum rank problems in graph theory
This thesis regards the minimum rank and minimum positive semidefinite rank of a simple graph. A graph parameter, called the minimum labeling degree (mld), is defined in terms of the concept of a vertex labeling of a graph, and its value is calculated for a few graph classes. It is proved here that …
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Novel frameworks for auctions and optimization
… barriers on the running time used for solving positive linear programs, (2) reduce the complexity for solving positive semidefinite programs, and (3) strengthen the theory of matrix multiplicative weight updates and improve the theory of linear-sized spectral sparsification.
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Constrained signal reconstruction
… problem of this type is the extrapolation of a positive semidefinite sequence, which is equivalent to the covariance extension and trigonometric moment problems. Classical results are extended to incorporate the additional convex constraints imposed by spectral support limits and bounding …
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On the numerical solution of continuous coupled algebraic Riccati equations
… accelerated Riccati iteration which computes a positive semidefinite solution of the continuous coupled algebraic Riccati equation. In particular, we establish sufficient conditions for the convergence of this algorithm. We also prove that for particular initial values this algorithm determines …
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Adversarial Two-Party Quantum Interactions in Cryptography and Machine Learning
… bound for learning over general subsets of positive semidefinite matrices via the regularized follow-the-leader algorithm and apply it to various settings involving the learning of quantum objects. For concrete applications, we present a sublinear regret bound for learning quantum states, …
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Cutting Planes for Convex Objective Nonconvex Optimization
… In the special case where the objective is a positive definite quadratic function, polynomial time separation procedures using the new class of lifted inequalities are developed for the cases when the domain is the complement of the interior of a polyhedron, a union of polyhedra, or the …
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On the minimum rank of certain graphs with path cover number 2
… Recent work in zero-forcing parameters, minimum semidefinite rank, and ranks of outerplanar graphs have given more ways to calculate upper and lower bounds for the minimum rank of a graph. We define a family of graphs with path cover number two and consider restrictions on the structure and …
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Real Even Symmetric Forms
… proved that a form P $\in$ F$\sb{n,m}$ which is positive semidefinite (psd) must have a representation as a sum of squares (sos) of forms if and only if n = 2, m = 2, or (n,m) = (3,4). No concrete example of a psd form which is not sos was known until the late 1960's. We denote by …
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The power of randomized algorithms : from numerical linear algebra to biological systems
… randomized low-rank approximation algorithm for positive semidefinite matrices that runs in sublinear time, significantly improving upon what is possible with traditional deterministic methods. We also discuss lower bounds on low-rank approximation and spectral summarization problems that attempt …
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Integrating Multiple Data Views for Improved Malware Analysis
… The only restriction that must be met is that a positive semidefinite similarity (kernel) matrix must be defined on the view, a restriction that is easily met in practice. While the classification problem can be solved with well known multiple kernel learning techniques, the clustering and …
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Matrix Factorizations, Triadic Matrices, and Modified Cholesky Factorizations for Optimization
… a linear symmetric system Ax=b. When A is not positive definite, the computed search direction may not be a descent direction. Modified Newton methods add a perturbation E to A, so that A+E is positive definite, where E is symmetric positive semidefinite. We study the modified Newton methods in …
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Topological and geometric inference of data
… which relate several metrics on the space of positive semidefinite matrices; they are then interpreted in the context of topological data analysis. This is applied to diffusion tensor imaging and phonology. The final chapter explores the case where the points are non-uniformly distributed over …
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Polynomial Structure in Semidefinite Relaxations and Non-Convex Formulations
Semidefinite relaxation is a powerful tool used to approximate otherwise intractable non-convex problems, but tend to run into scalability issues in large-scale instances. The goal of this thesis is to explore the power of semidefinite relaxations and address the scalability issues, for special …
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Linear and ellipsoidal pattern separation: theoretical aspects and experimental analysis
… we experimentally test both algorithms on the positive semidefinite constraint satisfaction problem. Numerical results confirm our conjectures on the behaviour of the algorithms when the dimension of the problem grows. In the second part, we shift our focus from linear to ellipsoidal …
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Exact and variational investigations of Hubbard rings
… wave function. Because the 2-RDM must be positive semidefinite, we use an efficient programming algorithm known as the Semidefinite Programming Algorithm. A naive search through the space of two-particle matrices encounters a difficult problem, known as the " N -representability problem", …
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Quadratic maximization under combinatorial constraints and related applications
… argument matrix of the quadratic objective is positive semidefinite and has constant rank. Our approach relies on a hyper-spherical transformation of the low-rank space and has complexity that scales exponentially in the rank of the input, but polynomially in the ambient dimension. Extending …
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Addressing Missing Data and Scalable Optimization for Data-driven Decision Making
… optimal solutions in the context of approximate semidefinite programming. Specifically, we ask the question: “how closely can we approximate the set of unit-trace n × n positive semidefinite (PSD) matrices, denoted by Dⁿ, using at most N number of k × k PSD constraints?” We show that any set S …
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Kippenhahn's Conjecture: Counterexamples and Quantisation
… By requiring that the matrix thus defined be positive semidefinite, that is having no negative eigenvalues, a convex region called a spectrahedron is defined in the space of variables.Spectrahedra and linear pencils are the subject of a field of study known as semidefinite programming, which …
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Geometric optimization algorithms for linear regression on fixed-rank matrices
… both the learning of a fixed-rank symmetric positive semidefinite matrix and of a fixed-rank non-symmetric matrix. A first contribution of the thesis is to show that many modern machine learning problems can be formulated as linear regression problems on the set of fixed-rank matrices. For …
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