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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 46 for “"convex sets"”.
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Reconstructing convex sets
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1985.
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Counting Convex Sets on Products of Totally Ordered Sets
… purpose of this thesis is to find the number of convex sets on a product of two totally ordered spaces. We will give formulas to find this number for specific cases and describe a process to obtain this number for all such spaces. In the first chapter we briefly discuss the motivation behind the …
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Fast Multi-query Planning in Graphs of Convex Sets
Planning in Graphs of Convex Sets (GCS) is a recently developed optimization framework that seamlessly integrates discrete and continuous decision making. It naturally models and effectively solves a wide range of challenging planning problems in robotics, including collision-free motion planning, …
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Extremal Problems on Graph Structure, Coding Applications, and Convex Sets
Finally, we also prove an analogue to the Erdo&huml;s-Ko-Rado Theorem on Hamming code.
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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 high-order …
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Measures and Barycenters of Measures on Convex Sets in Locally Convex Spaces
Made available in DSpace on 2014-12-09T22:17:44Z (GMT). No. of bitstreams: 1 6812141.pdf: 2004987 bytes, checksum: 728b6517d6fbafa17d0bcc5c614ae9f9 (MD5) Previous issue date: 1968
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Graphs of Convex Sets with Applications to Optimal Control and Motion Planning
… problems at the interface of combinatorial and convex optimization. We consider graphs where each vertex is paired with a convex program, and each edge couples two programs through additional convex costs and constraints. We call such a graph a Graph of Convex Sets (GCS). Over a GCS we can …
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An Application of Graph of Convex Sets Trajectory Optimization to the Marine Robotics Domain
… the dynamic limits of the vehicle. The Graphs of Convex Sets (GCS) trajectory optimization motion planner from the MIT Robot Locomotion Group is a recently developed planner which has been demonstrated to return smooth and optimal paths navigating around complex environments filled with obstacles, …
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Approximate signal reconstruction from partial information
… a single basis. The method of Projection Onto Convex Sets (POCS) is used to reconstruct an approximation to the MBR signal using the side information. Thus, any number of constraints may be used as long as they form closed and convex sets and the side information is a priori knowledge required …
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The Hahn-Banach Separation Theorem in Free Convexity
… theorems on separation in the context of free convexity and matrix convex sets. After presenting a proof of the Hahn-Banach Separation Theorem, the main work in this thesis is a treatment of the Effros-Winkler Hahn-Banach Separation Theorem in the setting of matrix convex sets. This result is …
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Problems in Graph Coloring and Graph Structure
Let F be a family of translates of a fixed convex set in the plane, and let G be the intersection graph of F . We studied the chromatic number of the complement of G. We also studied the transversal number of F , where the transversal number is the minimum size of a set of points that intersects …
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Asymptotic phase diagrams for lattice spin systems
… there is a one-one correspondence between subsets of the phase diagram and extremal elements of some family of convex sets. We also solve a linear programming problem of the phase diagram for a set of affine functionals.
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Sums of Polynomials, Minmax Problems and Number Theory
… whether certain collections of planar convex sets are packings. This new method is successfully applied to other extremal problems. Moreover we study some minmax problems for fractional parts of real numbers.
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Algorithms above the noise floor
… practice. Common examples include optimizing non-convex functions or optimizing over non-convex sets. In theory, such problems are usually NP-hard. But in practice, they are often solved sufficiently well for applications in machine learning and statistics. Even when a problem is convex, we often …
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Implementation of Iterative Reconstruction of Images from Multiple Bases Representations
… by the iterative method of Projection onto Convex Sets (POCS). Many constraints that form convex sets are reviewed and examined. Due to the high distortion at the block boundaries, some constraints are introduced particularly to reduce artifacts at the boundaries. Some constraints add energy …
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Observations on Convexity
<p>This thesis will explore convexity as it pertains to sets of complex-valued functions. These include preliminary looks at established linear and polynomially convex hulls, along with the development of new types of convex hulls. These types will include, but are not limited to the hulls …
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β-Uniform Convexity and Divisible Domains
Divisible convex sets have long been important in the study of Hilbert geometries. When a divisible convex set is an ellipsoid, the Hilbert geometry it induces is the hyperbolic space. In general, strictly convex divisible domains exhibit negative curvature properties, but only the ellipsoid is a …
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Optimal estimation in high-dimensional and nonparametric models
… chapter, a new estimator for the volume of a convex set is proposed. The estimator is minimax optimal and also efficient non-asymptotically: it is nearly unbiased with minimal variance among all unbiased oracle-type estimators. Our approach is based on a Poisson point process model and as an …
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