Nonlinear Programming: Theory and AlgorithmsPresents recent developments of key topics in nonlinear programming using a logical and self-contained format. Divided into three sections that deal with convex analysis, optimality conditions and duality, computational techniques. Precise statements of algorithms are given along with convergence analysis. Each chapter contains detailed numerical examples, graphical illustrations and numerous exercises to aid readers in understanding the concepts and methods discussed. |
Contents
Introduction | 1 |
Convex Sets | 33 |
Convex Functions and Generalizations | 78 |
Copyright | |
11 other sections not shown
Common terms and phrases
algorithm Applications approach approximation assume assumption called Chapter closed complementary computational Consider the following constraint qualification constraints continuous convergence convex set defined denoted derivative differentiable direction discussed duality equal equivalent Example Exercise exists extreme point feasible feasible solution Figure following problem Furthermore given gives gradient Hence holds illustrated implies inequality interval iteration KKT conditions Lagrangian line search linear programming Mathematical Programming matrix maximum method minimize f(x Minimize subject multipliers necessary nonempty Nonlinear Programming Note objective function obtained Operations optimal optimal solution Otherwise penalty function positive definite primal problem to minimize procedure programming problem proof Quadratic Programming quasiconvex reduced referred region replace Research result satisfies sequence Show simplex method solution solving starting step strictly sufficient suppose symmetric matrix Theorem true variables vector Vf(x x₁ zero