Classical optimization - unconstrained and equality constrained problems; Optimality conditions for constrained extrema; Convex sets and functions; Duality in nonlinear convex programming; Generalized convexity; Analysis of selected nonlinear programming problems; One-dimensional optimization; Multidimensional unconstrained optimization without derivative: empirical and conjugate direction methods; Second derivative, steepest descent and conjugate gradient methods; Variable metric algorithms; Penalty function methods; Solution of constrained problems by extensions of unconstrained optimization techniques; Approximation-type algorithms.
An important result in combinatorial analysis is known as Koenig's Theorem . Theorem 6.1 . Koenig's Theorem . For any matrix A and its set Z of zero positions Independence order = Covering index . ( 6.25 ) This theorem can be ...
This monograph uses braids to explore dynamics on surfaces, with an eye towards applications to mixing in fluids. The text uses the particular example of taffy pulling devices to represent...
This work addresses the problem of minimizing or maximizing a linear function in the presence of linear equality or inequality constraints. It provides methods for modeling complex problems via effective...
Mathematical programming: an overview; solving linear programs; sensitivity analysis; duality in linear programming; mathematical programming in practice; integration of strategic and tactical planning in the aluminum industry; planning the mission...
This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text.
This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations. There are carefully analyzed logistic type equations with boundary blow-up solutions and...
The only book to treat both linear programming techniques and network flows under one cover, this book has been conpletely updated with the latest developments on the topic. This new...
Nonlinear Programming
Applied Nonlinear Programming
Introduction to nonlinear programming; Review of linear programming; Further mathematical background; Classical uncostrained optimization; Optimum-seeking by experimentation; Lagrange multipliers and kuhn-tucker theory; Quadratic programming; Algorithms for linearly constrained problems; Algorithms...