Методы оптимизации
Математика
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Antoniou A., Lu W.-S. Practical Optimization. Algorithms and Engineering Applications
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 tu, motivated widespread applications of optimization methods in many disciplines, e.g., engineering, business, and science, and led to problem solutions that were considered intractable not too long ago.
Although excellent books are available that treat the subject of optimization with great mathematical rigor and precision, there appears to be a need for a book that provides a practical treatment of the subject aimed at a broader audience ranging from college students to scientists and industry professionals. This book has been written to address this need. It treats unconstrained and constrained optimization in a unified manner and places special attention on the algorithmic aspects of optimization to enable readers to apply the various algorithms and methods to specific problems of interest. To facilitate this process, the book provides many solved examples that illustrate the principles involved, and includes, in addition, two chapters that deal exclusively with applications of unconstrained and constrained optimization methods to problems in the areas of patte recognition, control systems, robotics, communication systems, and the design of digital filters. For each application, enough background information is provided to promote the understanding of the optimization algorithms used to obtain the desired solutions.

The optimization problem.
basic principles.
General properties of algorithms.
One-Dimensional optimization.
basic multidimensional gradient methods.
Conjugate-Direction methods.
Quasi-neWton methods.
Minimax methods.
Applications of unconstrained optimization.
Fundamentals of constrained optimization.
Linear programming part i: The simplex method.
Linear programming part iI: Interior-Point methods.
Quadratic and convex programming.
Semidefinite and second-Order cone programming.
General nonlinear optimization problems.
Applications of constrained optimization.
a basics of Linear Algebra.
B basics of Digital Filters.
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