Optimization: Theory and Engineering Applications

Description

A modern term for operations research, called Optimization Theory. It is a branch of mathematics which encompasses many diverse areas of minimization and optimization. Mathematically, most of the interesting optimization problems can be formulated to optimize some objective function, subject to some equality and inequality constraints. This book “Optimization Theory and Engineering Applications” introduces some classical and basic results of optimization theory, including nonlinear programming with Lagrange multiplier method, the Karush-Kuhn-Tucker method, Fritz John's method, problems with convex or quasi-convex constraints, and linear programming with geometric method and simplex method. It also systematically describes optimization theory and several powerful methods, including recent results. For most methods, the authors discuss an idea's motivation, study the derivation, establish the global and local convergence, describe algorithmic steps, and discuss the numerical performance. This book is intended for senior students, graduates, teachers, and researchers in optimization, operations research, computational mathematics, applied mathematics, and some engineering and economics. It will also be useful for scientists in engineering and economics.