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Showing 1 to 9 of 9 for “"sparse optimization"”.
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First Order Methods for Large-Scale Sparse Optimization
… large-scale applications can be modeled as optimization problems with millions of decision variables. Very often, the desired solution is sparse in some form, either because the optimal solution is indeed sparse, or because a sparse solution has some desirable properties. Sparse and low-rank …
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Flows, Submodularity, Sparsity, and Beyond: Continuous Optimization Insights for Discrete Problems
… on connections between discrete and continuous optimization. In the first part of the thesis we propose faster second-order convex optimization algorithms for classical graph algorithmic problems. Our main contribution is to show that the runtime of interior point methods is closely connected to …
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Enhancing Generalization in Sketch-Based Image Retrieval through Single and Multi-Source Domain Adaptation
… alongside dictionary learning principles and sparse optimization techniques to facili- tate effective knowledge transfer from a source (e.g., images) to a target domain (e.g., sketches), even in few-shot scenarios . This approach is further extended to a multi-source domain adapta- tion …
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Large-Scale Optimization Methods: Theory and Applications
Large-scale optimization problems appear quite frequently in data science and machine learning applications. In this thesis, we show the efficiency of coordinate descent (CD) and mirror descent (MD) methods in solving large-scale optimization problems. First, we investigate the convergence rate of …
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From image co-segmentation to discrete optimization in computer vision - the exploration on graphical model, statistical physics, energy minimization, and integer programming
… ideas and frameworks for solving the discrete optimization problem in computer vision. Much of the work is inspired by the study of the image co-segmentation problem. It is through the research on this topic that the author has become very familiar with the graphical model and energy …
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On sparse mirror descent
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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Algorithms for Sparse and Low-Rank Optimization: Convergence, Complexity and Applications
Solving optimization problems with sparse or low-rank optimal solutions has been an important topic since the recent emergence of compressed sensing and its matrix extensions such as the matrix rank minimization and robust principal component analysis problems. Compressed sensing enables one to …
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Optimization Techniques Exploiting Problem Structure: Applications to Aerodynamic Design
… a Reduced Hessian formulation which projects the optimization problem to a lower dimension design space. The second method exploits the sparse structure in a given problem which can yield significant savings in terms of computational effort as well as storage requirements. An underlying theme in …
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Structured Sparsity Promoting Functions: Theory and Applications
<p>Motivated by the minimax concave penalty based variable selection in high-dimensional linear regression, we introduce a simple scheme to construct structured semiconvex sparsity promoting functions from convex sparsity promoting functions and their Moreau envelopes. Properties of these functions …