Ebook: Practical mathematical optimization: an introduction to basic optimization theory and classical and new gradient-based algorithms

"This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form without neglecting rigour. The work should enable the professional to apply optimization theory and algorithms to his own particular practical field of interest, be it engineering, physics, chemistry, or business economics. Most importantly, for the first time in a relatively brief and introductory work, due attention is paid to the difficulties - such as noise, discontinuities, expense of function evaluations, and the existence of multiple minima - that often unnecessarily inhibit the use of gradient-based methods. In a separate chapter on new gradient-based methods developed by the author and his coworkers, it is shown how these difficulties may be overcome without losing the desirable features of classical gradient-based methods." "It is intended that this book be used in senior- to graduate-level semester courses in optimization, as offered in mathematics, engineering, computer science, and operations research departments, and also to be useful to practising professionals in the workplace.";What is mathematical optimization? -- Objective and constraint functions -- Basic optimization concepts -- Further mathematical prerequisites -- Unconstrained minimization -- Line search descent methods for unconstrained minimization : general line search descent algorithm for unconstrained minimization -- One-dimensional line search -- First order line search descent methods -- Second order line search descent methods -- Zero order line search descent methods -- Zero order methods and computer optimization subroutines -- Test functions -- Standard methods for constrained optimization -- Penalty function methods for constrained minimization -- Classical methods for constrained optimization problems -- Saddle point theory and duality -- Quadratic programming -- Modern methods for constrained optimization -- New gradient-based trajectory and approximation methods -- The dynamic trajectory optimization methods -- The spherical quadratic steepest descent method -- The dynamic-Q optimization algorithm -- A gradient-only line search method for conjugate gradient methods -- Global optimization using dynamic search trajectories -- Example problems : Line search descent methods, standard methods for constrained optimization -- Some theorems : Characterization of functions and minima -- Equality constrained problem -- Karush-Kuhn-Tucker theory -- Saddle point conditions -- Conjugate gradient methods -- DFP method -- The simplex method for linear programming problems -- Pivoting for increase in objective function -- The auxiliary problem for problem with infeasible origin -- Example of auxiliary problem solution -- Degeneracy -- The revised simplex method -- An iteration of the RSM.