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An Introduction to Continuous Optimization
 
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Author : Niclas Andreasso Anton Evgrafov Michael Patriksson
Subject / Year : Mathematics / 2006
Publisher : Overseas Press India Pvt. Ltd.
ISBN : 13- 9788188689507 10- 8188689505
Price : INR 995.00
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Description
Contents
 I Introduction
Modelling and classification - Modelling of optimization problems, A quick glance at optimization history, Classification of optimization models, Conventions, Applications and modelling examples, Defining the field, On optimality conditions, Soft and hard constraints,  A road map through the material, On the background of this book and a didactics statement, Illustrating the theory, Notes and further reading, Exercises,
 II Fundamentals
Analysis and algebra—A summary - Reductio ad absurdum, Linear algebra, Analysis
Convex analysis -  Convexity of sets, Polyhedral theory, Convex functions, Application: the projection of a vector onto a convex set, Notes and further reading, Exercises
 III Optimality Conditions
An introduction to optimality conditions -  Local and global optimality, Existence of optimal solutions, Optimality in unconstrained optimization, Optimality for optimization over convex sets, Near-optimality in convex optimization,  Applications, Notes and further reading, Exercises
Optimality conditions - Relations between optimality conditions and CQs at a glance,  A note of caution, Geometric optimality conditions, The Fritz John conditions, The Karush–Kuhn–Tucker conditions, Proper treatment of equality constraints, Constraint qualifications, Sufficiency of the KKT conditions under convexity,  Applications and examples, Notes and further reading, Exercises
Lagrangian duality - The relaxation theorem, Lagrangian duality, Differentiability properties of the dual function,  *Subgradient optimization methods,  *Obtaining a primal solution, *Sensitivity analysis, Applications,
Notes and further reading, Exercises
 IV Linear Programming
Linear programming: An introduction - The manufacturing problem,  A linear programming model, Graphical solution, Sensitivity analysis, The dual of the manufacturing problem,
Linear programming models - Linear programming modelling, The geometry of linear programming, Notes and further reading, Exercises
The simplex method - The algorithm, Termination, Computational complexity, Notes and further reading, Exercises
LP duality and sensitivity analysis - Introduction, The linear programming dual, Linear programming duality theory, The dual simplex method, Sensitivity analysis, Notes and further reading, Exercises
V Algorithms
Unconstrained optimization - Introduction, Descent directions, The line search problem, Convergent algorithms, Finite termination criteria, A comment on non-differentiability,Trust region methods, Conjugate gradient methods, A quasi-Newton method: DFP, Convergence rates, Implicit functions, Notes and further reading, Exercises
Optimization over convex sets - Feasible direction methods, The Frank–Wolfe algorithm, The simplicial decomposition algorithm, The gradient projection algorithm, Application: traffic equilibrium, Notes and further reading, Exercises
Constrained optimization - Penalty methods, Sequential quadratic programming, A summary and comparison, Notes and further reading, Exercises
VI Appendix
A Answers to the exercises - Modelling and classification, Convexity, An introduction to optimality conditions, Optimality conditions, Lagrangian duality, Linear programming models, The simplex method, LP duality and sensitivity analysis, Unconstrained optimization,Optimization over convex sets, Constrained optimization
References
Index
 
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