Haslinger J., M?kinen R.A.E. Introduction to shape optimization: theory, approximation, and computation

Издательство Springer, 2007, -675 pp. The rapid advancements in the efficiency of digital computers and the evolution of reliable software for numerical computation during the past three decades have led to an astonishing growth in the theory, methods, and algorithms of numerical optimization. This body of knowledge has, in turn, motivated widespread applications of optimization methods in many disciplines, e.g., engineering, business, and scien...

Springer, 2008. 211 p. Mechanical and structural engineers have always strived to make as efficient use of material as possible, e.g. by making structures as light as possible yet able to carry the loads subjected to them. In the past, the search for more efficient structures was a trial-and-error process. However, in the last two decades computational tools based on optimization theory have been developed that make it possible to find optimal s...

Springer | 2011 | ISBN: 1441964908 | 683 pages The book is designed for use in courses that focus on the applications of constrained optimization, in courses that emphasize the theory, and in courses that link the subject to economics. It surveys models that optimize something, subject to constraints. The simplest such models are linear, and the ideas used to analyze linear models generalize easily. The book fuses five components: It uses exampl...

Publisher: Society for Industrial Mathematics | 2008 | ISBN10: 0898716438 | 280 pages MPS-SIAM Series on Optimization This textbook provides a self-contained introduction to linear programming using MATLAB® software to elucidate the development of algorithms and theory. Early chapters cover linear algebra basics, the simplex method, duality, the solving of large linear problems, sensitivity analysis, and parametric linear programming. In later ch...

Springer, 2007. 296 pages. This book presents an application-oriented introduction to the theory of nonlinear optimization. It describes basic notions and conceptions of optimization in the setting of normed or even Banach spaces. Various theorems are applied to problems in related mathematical areas. For instance, the Euler-Lagrange equation in the calculus of variations, the generalized Kolmogorov condition and the alternation theorem in approx...

Издательство Springer, 2006, -595 pp. Combinatorial optimization is one of the youngest and most active areas of discrete mathematics, and is probably its driving force today. It became a subject in its own right about 50 years ago. This book describes the most important ideas, theoretical results, and algorithms in combinatorial optimization. We have conceived it as an advanced graduate text which can also be used as an up-to-date reference wor...

John Wiley & Sons, 2009. 813 p. 4th ed. ISBN 978-0-470-18352-6. Contents. Preface. Introduction to Optimization. Classical Optimization Techniques. Linear Programming I: Simplex Method. Linear Programming II: Additional Topics and Extensions. Nonlinear Programming I: One-Dimensional Minimization Methods. Nonlinear Programming II: Unconstrained Optimization Techniques. Nonlinear Programming III: Constrained Optimization Techniques. Geometric P...

Only in Engllish, Princeton University Press. Discussed unconstrained optimization problem with nonlinear optimization models, nonlinear optimization theory, and numerical methods of optimization (for instance, quadratic programming problems).

Springer,2005 1. Introduction What is mathematical optimization? Objective and constraint functions Basic optimization concepts Further mathematical prerequisites Unconstrained minimization Line search descent mtthods for uncinstrained mininization 2. 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 o...

Springer-Verlag, 1992. P. 250 This book presents modern functional analytic methods for the sensitivity analysis of some infinite-dimensional systems governed by partial differential equations. The main topics are treated in a general and systematic way. They include many classical applications such as the Signorini Problem, the elastic-plastic torsion problem and the visco-elastic-plastic problem. The "material derivative" from which any kind of...