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 25 for “"first-order methods"”.
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Fast distributed first-order methods
… and analysis of distributed optimization methods for multi-agent networks with time-varying connectivity. The goal is to optimize a global objective function which is the sum of local objective functions privately known to individual agents. In our methods, each agent iteratively updates …
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First Order Methods for Large-Scale Sparse Optimization
… data matrices. Therefore, interior point based methods are ill-suited for solving these problems. The large scale of these problems forces one to use the so-called first-order methods that only use gradient information at each iterate. These methods are efficient for problems with a "simple" …
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Novel first-order methods for bilevel and minimax optimization.
… and bilevel optimization and develops novel first-order methods with strong theoretical guarantees for solving both classes of problems. Specifically, we study a class of constrained minimax problems and propose efficient augmented Lagrangian methods with complexity guarantees for both …
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Efficient learning of temporal dynamics with first-order methods
… efficient, by harnessing the power of first-order optimization methods. In particular, we provide solutions to the above challenges, by developing the following distinct, yet closely related algorithms: • First, we introduce an online learning framework for nonparametric maximum …
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On the Complexity of Nonconvex-Strongly-Concave Smooth Minimax Optimization Using First-Order Methods
… minimax optimization using first-order methods. First, we provide a first-order oracle complexity lower bound for finding stationary points of nonconvex-strongly-concave smooth min-max optimization problems. We establish a lower bound of Ω ( √ 𝜅𝜖⁻²) for deterministic oracles, …
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Accelerated first-order optimization methods using inertia and error bounds
… machine learning applications. The focus is on first-order methods which have low per-iteration complexity and can exploit problem structure to a high degree. First-order methods have the capacity to address large-scale problems for which all alternative methods fail. However, first-order …
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Advances in Computer-Assisted Design and Analysis of First-Order Optimization Methods and Related Problems
First-order methods are optimization algorithms that can be described and analyzed using the values and gradients of the functions to be minimized. These methods have become the main workhorses for modern large-scale optimization and machine learning due to their low iteration costs, minimal memory …
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Methods for convex optimization and statistical learning
… several contributions at the interface of first-order methods for convex optimization and problems in statistical machine learning. In the first part of this thesis, we present new results for the Frank-Wolfe method, with a particular focus on: (i) novel computational guarantees that apply …
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New Theory and Algorithms for Convex Optimization with Non-Standard Structures
… of science and engineering. In recent years, first-order methods have played important roles in tackling applications arising in machine learning and data science, due to their simplicity, reasonably fast convergence rate, and low periteration computational cost. However, there exist many …
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Novel frameworks for auctions and optimization
… II introduces novel frameworks for understanding first-order methods in optimization. This enables us to (1) break 20-year 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 …
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Robust accelerated gradient methods for machine learning
… this optimization problem, we consider using first order methods which are popular due to their scalability with large data sets, and we study the case that the exact gradient information is not available. In this setting, a naive implementation of classical first order algorithms need not …
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Large-scale optimization Methods for data-science applications
… contributions of large scale optimization methods with the applications in data science and machine learning. In the first part, we present new computational methods and associated computational guarantees for solving convex optimization problems using first-order methods. We consider …
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Topics in non-convex optimization and learning
… optimization and deep neural networks. In the first part, I develop iteration complexity analysis for Riemannian optimization, i.e., optimization problems defined on Riemannian manifolds. Through bounding the distortion introduced by the metric curvature, iteration complexity of Riemannian …
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Sparse learning : statistical and optimization perspectives
… from areas of convex and discrete optimization. First, we explore an Lq-regularized version of the Best Subset selection procedure which mitigates the poor statistical performance of the best-subsets estimator in the low SNR regimes. The statistical and empirical properties of the estimator are …
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A compressed sensing approach to block-iterative equalization: connections and applications to radar imaging reconstruction
… higher performance when compared to existing methods. Our reasoning will also show that a properly formulated BI-DFE turns out to be a powerful CS algorithm itself. A new algorithm, referred to as CS-Block DFE (CS-BDFE) exhibits improved convergence and detection when compared to first order …
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Statistical aspects of optimal transport
… estimation. In the Gaussian case, we analyze first-order methods for computing barycenters, and develop global, dimension-free rates of convergence despite the non-convexity of the problem. Extending beyond the Gaussian case, however, is challenging due to the fundamental curse of …
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Stochastic structural analysis of engineering components using the finite element method
… thesis investigates probabilistic and stochastic methods for structural analysis which can be integrated into existing, commercially available finite element programs. It develops general probabilistic finite element routines which can be implemented within deterministic finite element programs …
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Polynomial Structure in Semidefinite Relaxations and Non-Convex Formulations
… of problems with polynomial structure. In the first part of this thesis, we consider semidefinite relaxations of functions on quadratic maps, with applications to approximating permanents of positive semidefinite (PSD) matrices, product of quadratic forms, and can be interpreted as a …
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Semiparametric Approaches for Dimension Reduction Through Gradient Descent on Manifold
… high-dimensional data. We develop several SDR methods through manifold parameterization. First, we propose a SDR method, gemDR, based on local kernel regression without loss of information of the conditional mean E[Y|X]. The method, gemDR, focuses on identifying the central mean subspace (CMS). …
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New Theory and New Practical Methods for Solving Large-Scale Linear and Conic Optimization
… (LPs) are solved in practice, with classic methods (simplex method and interior-point methods) being replaced by the primal-dual hybrid gradient method (PDHG) to solve large-scale LP problems. While PDHG---with heuristic enhancements and GPU implementation---has been very successful in …
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