Algorithmic Principles of Mathematical ProgrammingSpringer Science & Business Media, 17 thg 4, 2013 - 339 trang Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature. The book is equally suited for self-study for a motivated beginner and for a comprehensive course on the principles of mathematical programming within an applied mathematics or computer science curriculum at advanced undergraduate or graduate level. The presentation of the material is such that smaller modules on discrete optimization, linear programming, and nonlinear optimization can easily be extracted separately and used for shorter specialized courses on these subjects. |
Nội dung
Linear Equations and Linear Inequalities | 21 |
Polyhedra | 55 |
Linear Programs and the Simplex Method | 71 |
Lagrangian Duality | 95 |
An Interior Point Algorithm for Linear Programs | 109 |
Network Flows | 123 |
Complexity | 153 |
Integer Programming | 173 |
Convex Sets and Convex Functions | 197 |
Unconstrained Optimization | 241 |
Constrained Nonlinear Optimization | 273 |
List of frequently used Symbols | 325 |
Ấn bản in khác - Xem tất cả
Algorithmic Principles of Mathematical Programming Ulrich Faigle,W. Kern,Georg Still Xem trước bị giới hạn - 2002 |
Algorithmic Principles of Mathematical Programming Ulrich Faigle,W. Kern,G. Still Không có bản xem trước - 2014 |
Algorithmic Principles of Mathematical Programming Ulrich Faigle,W. Kern,G. Still Không có bản xem trước - 2002 |
Thuật ngữ và cụm từ thông dụng
a₁ assume augmenting path basic solution bounded c¹x column compute cone consider constraints conv convergence convex function convex set Corollary corresponding defined denote derive descent direction descent method differentiable dual feasible duality edges efficient Ellipsoid Method equality equations equivalent exists Farkas Lemma feasible direction feasible solution finite function f Gaussian elimination global gradient graph graph coloring Hence holds hyperplane implies inequality inner product integer interior point method iteration KKT-conditions KKT-point Lemma LICQ linear program matrix maximizer minimizer multipliers node objective function obtain optimal solution optimality conditions optimization problem parameters pivot polyhedron polynomial positive definite Proof quadratic REMARK resp Rmxn satisfies Section semidefinite semidefinite program Show simplex algorithm simplex method solve step strictly feasible subgradient subset symmetric matrix system Ax Theorem unique variables Vƒ(x x₁ Xk+1 y¹A y¹g(x yields