Nonlinear Programming Analysis and Methods

Nonlinear Programming : Analysis and Methods. By Avriel, Mordecai
2012 | 1075 Pages | ISBN: 0486151670 | EPUB | 29 MB
DOVER BOOKS ON MATHEMATICS; Title Page; Copyright Page; Dedication; ABOUT THE AUTHOR; Table of Contents; PREFACE; 1 INTRODUCTION; PART I - ANALYSIS; 2 - CLASSICAL OPTIMIZATION-UNCONSTRAINED AND EQUALITY CONSTRAINED PROBLEMS; 2.1 UNCONSTRAINED EXTREMA; 2.2 EQUALITY CONSTRAINED EXTREMA AND THE METHOD OF LAGRANGE; 3 - OPTIMALITY CONDITIONS FOR CONSTRAINED EXTREMA; 3.1 FIRST-ORDER NECESSARY CONDITIONS FOR INEQUALITY CONSTRAINED EXTREMA; 3.2 SECOND-ORDER OPTIMALITY CONDITIONS; 3.3 SADDLEPOINTS OF THE LAGRANGIAN; 4 - CONVEX SETS AND FUNCTIONS; 4.1 CONVEX SETS; 4.2 CONVEX FUNCTIONS.4.3 DIFFERENTIAL PROPERTIES OF CONVEX FUNCTIONS4.4 EXTREMA OF CONVEX FUNCTIONS; 4.5 OPTIMALITY CONDITIONS FOR CONVEX PROGRAMS; 5 - DUALITY IN NONLINEAR CONVEX PROGRAMMING; 5.1 CONJUGATE FUNCTIONS; 5.2 DUAL CONVEX PROGRAMS; 5.3 OPTIMALITY CONDITIONS AND LAGRANGE MULTIPLIERS; 5.4 DUALITY AND OPTIMALITY FOR STANDARD CONVEX PROGRAMS; 6 - GENERALIZED CONVEXITY; 6.1 QUASICONVEX AND PSEUDOCONVEX FUNCTIONS; 6.2 ARCWISE-CONNECTED SETS AND CONVEX-TRANSFORMABLE FUNCTIONS; 6.3 LOCAL AND GLOBAL MINIMA; 7 - ANALYSIS OF SELECTED NONLINEAR PROGRAMMING PROBLEMS; 7.1 QUADRATIC PROGRAMMING.7.2 STOCHASTIC LINEAR PROGRAMMING WITH SEPARABLE RECOURSE FUNCTIONS7.3 GEOMETRIC PROGRAMMING; PART II - METHODS; 8 - ONE-DIMENSIONAL OPTIMIZATION; 8.1 NEWTON'S METHOD; 8.2 POLYNOMIAL APPROXIMATION METHODS; 8.3 DIRECT METHODS-FIBONACCI AND GOLDEN SECTION TECHNIQUES; 8.4 OPTIMAL AND GOLDEN BLOCK SEARCH METHODS; 9 - MULTIDIMENSIONAL UNCONSTRAINED OPTIMIZATION WITHOUT DERIVATIVES: EMPIRICAL AND CONJUGATE DIRECTION METHODS; 9.1 THE SIMPLEX METHOD; 9.2 PATTERN SEARCH; 9.3 THE ROTATING DIRECTIONS METHOD; 9.4 CONJUGATE DIRECTIONS; 9.5 POWELL'S METHOD; 9.6 AVOIDING LINEARLY DEPENDENT SEARCH DIRECTIONS.9.7 FURTHER CONJUGATE DIRECTION-TYPE ALGORITHMS10 - SECOND DERIVATIVE, STEEPEST DESCENT, AND CONJUGATE GRADIENT METHODS; 10.1 NEWTON-TYPE AND STEEPEST DESCENT METHODS; 10.2 CONJUGATE GRADIENT METHODS; 10.3 CONVERGENCE OF CONJUGATE GRADIENT ALGORITHMS; 11 - VARIABLE METRIC ALGORITHMS; 11.1 A FAMILY OF VARIABLE METRIC ALGORITHMS; 11.2 QUASI-NEWTON METHODS; 11.3 VARIABLE METRIC ALGORITHMS WITHOUT DERIVATIVES; 11.4 MINIMIZATION METHODS BASED ON NONQUADRATIC FUNCTIONS; 12 - PENALTY FUNCTION METHODS; 12.1 EXTERIOR PENALTY FUNCTIONS; 12.2 INTERIOR PENALTY FUNCTIONS.12.3 PARAMETER-FREE PENALTY METHODS12.4 EXACT PENALTY FUNCTIONS; 12.5 MULTIPLIER AND LAGRANGIAN METHODS; 12.6 SOME COMPUTATIONAL ASPECTS OF PENALTY FUNCTION METHODS; 13 - SOLUTION OF CONSTRAINED PROBLEMS BY EXTENSIONS OF UNCONSTRAINED OPTIMIZATION TECHNIQUES; 13.1 EXTENSIONS OF EMPIRICAL METHODS; 13.2 GRADIENT PROJECTION ALGORITHMS FOR LINEAR CONSTRAINTS; 13.3 A QUADRATIC PROGRAMMING ALGORITHM; 13.4 FEASIBLE DIRECTION METHODS; 13.5 PROJECTION AND FEASIBLE DIRECTION METHODS FOR NONLINEAR CONSTRAINTS; 14 - APPROXIMATION-TYPE ALGORITHMS; 14.1 METHODS OF APPROXIMATION PROGRAMMING.Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This g.