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:Derivative-based Methods of OptimizationDirect Search Methods of OptimizationBasics of Riemannian Differential GeometryGeometric methods of optimization using Riemannian Langevin DynamicsStochastic Analysis on Manifolds and Geometric Optimization MethodsThis 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 main or supplementary texts for courses on classical and geometric optimization.

Debasish Roy, Professor, Department of Civil Engineering, Indian Institute of Science, Bangalore. He obtained his Ph.D. from the Indian Institute of Science, followed by post-doctoral research at the University of Innsbruck, Austria. He has published over 140 research papers in journals of national and international repute. His current research areas include geometrically inspired and gauge theories for continuum mechanics of solids, non-equilibrium thermodynamics of solids and fluctuation relations valid far from equilibrium, defect engineering and metamaterials with acoustic band gaps and optimization based on stochastic search on Riemannian manifolds.G. Visweswara Rao is currently working as an engineering consultant in Bangalore, India. He received his Ph.D. from the Indian Institute of Science, Bangalore, in 1989. He has published several research papers in the areas of structural dynamics specific to earthquake engineering, nonlinear and random vibration, and structural control. His areas of research include non-linear and stochastic structural dynamics.