Three abstract optimization problems are presented along with doubly iterative algorithms for their numerical solution. These algorithms are generalizations of particular algorithms described by Barr and Gilbert [19],...
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Three abstract optimization problems are presented along with doubly iterative algorithms for their numerical solution. These algorithms are generalizations of particular algorithms described by Barr and Gilbert [19], [21] and Fujisawa and Yasuda [22]. The supporting theory is fully developed along with proofs of convergence. Practical aspects of computations are considered and procedures which insure rapid convergence are discussed. Two applications to discrete-time optimal control problems are described.
This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates ...
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ISBN:
(数字)9783031130786
ISBN:
(纸本)9783031130779;9783031130809
This monograph presents a comprehensive treatment of the maximum-entropy sampling problem (MESP), which is a fascinating topic at the intersection of mathematical optimization and data science. The text situates MESP in information theory, as the algorithmic problem of calculating a sub-vector of pre-specificed size from a multivariate Gaussian random vector, so as to maximize Shannon's differential entropy. The text collects and expands on state-of-the-art algorithms for MESP, and addresses its application in the field of environmental monitoring. While MESP is a central optimization problem in the theory of statistical designs (particularly in the area of spatial monitoring), this book largely focuses on the unique challenges of its algorithmic side. From the perspective of mathematical-optimization methodology, MESP is rather unique (a 0/1 nonlinear program having a nonseparable objective function), and the algorithmic techniques employed are highly non-standard. In particular, successful techniques come from several disparate areas within the field of mathematical optimization; for example: convex optimization and duality, semidefinite programming, Lagrangian relaxation, dynamic programming, approximation algorithms, 0/1 optimization (e.g., branch-and-bound), extended formulation, and many aspects of matrix theory. The book is mainly aimed at graduate students and researchers in mathematical optimization and data analytics.
This book constitutes the refereed proceedings of the 19th Brazilian Symposium on Artificial Intelligence, SBIA 2008, held in Salvador, Brazil, in October 2008. The 27 revised full papers presented together with 3 inv...
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ISBN:
(数字)9783540881902
ISBN:
(纸本)9783540881896
This book constitutes the refereed proceedings of the 19th Brazilian Symposium on Artificial Intelligence, SBIA 2008, held in Salvador, Brazil, in October 2008.
The 27 revised full papers presented together with 3 invited lectures and 3 tutorials were carefully reviewed and selected from 142 submissions. The papers are organized in topical sections on computer vision and pattern recognition, distributed AI: autonomous agents, multi-agent systems and game knowledge representation and reasoning, machine learning and data mining, natural language processing, and robotics.
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