Elements Of Classical And Geometric Optimization
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Elements of Classical and Geometric Optimization
This comprehensive textbook covers both classical and geometric aspects of optimization using methods, deterministic and stochastic, in a single volume and in a language accessible to non-mathematicians. It will help serve as an ideal study material for senior undergraduate and graduate students in the fields of civil, mechanical, aerospace, electrical, electronics, and communication engineering. The book includes: Derivative-based Methods of Optimization. Direct Search Methods of Optimization. Basics of Riemannian Differential Geometry. Geometric Methods of Optimization using Riemannian Langevin Dynamics. Stochastic Analysis on Manifolds and Geometric Optimization Methods. This textbook comprehensively treats both classical and geometric optimization methods, including deterministic and stochastic (Monte Carlo) schemes. It offers an extensive coverage of important topics including derivative-based methods, penalty function methods, method of gradient projection, evolutionary methods, geometric search using Riemannian Langevin dynamics and stochastic dynamics on manifolds. The textbook is accompanied by online resources including MATLAB codes which are uploaded on our website. The textbook is primarily written for senior undergraduate and graduate students in all applied science and engineering disciplines and can be used as a main or supplementary text for courses on classical and geometric optimization.
Computing and Software Science
The papers of this volume focus on the foundational aspects of computer science, the thematic origin and stronghold of LNCS, under the title “Computing and Software Science: State of the Art and Perspectives”. They are organized in two parts: The first part, Computation and Complexity, presents a collection of expository papers on fashionable themes in algorithmics, optimization, and complexity. The second part, Methods, Languages and Tools for Future System Development, aims at sketching the methodological evolution that helps guaranteeing that future systems meet their increasingly critical requirements. Chapter 3 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Twentieth Anniversary Volume: Discrete & Computational Geometry
Author: Jacob E. Goodman
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-03-02
While we were busy putting together the present collection of articles celebrating the twentieth birthday of our journal, Discrete & Computational Geometry, and, in a way, of the ?eld that has become known under the same name, two more years have elapsed. There is no doubt that DCG has crossed the line between childhood and adulthood. By the mid-1980s it became evident that the solution of many algorithmic qu- tions in the then newly emerging ?eld of computational geometry required classical methodsandresultsfromdiscreteandcombinatorialgeometry. Forinstance,visibility and ray shooting problems arising in computer graphics often reduce to Helly-type questions for line transversals; the complexity (hardness) of a variety of geometric algorithms depends on McMullen’s upper bound theorem on convex polytopes or on the maximum number of “halving lines” determined by 2n points in the plane, that is, the number of different ways a set of points can be cut by a straight line into two parts of the same size; proximity questions stemming from several application areas turn out to be intimately related to Erdos’ ? s classical questions on the distribution of distances determined by n points in the plane or in space. On the other hand, the algorithmic point of view has fertilized several ?elds of c- vexity and of discrete geometry which had lain fallow for some years, and has opened new research directions.