Nonlinear programming: theory and algorithms
Presents 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.
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Convex Functions and Generalizations
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algorithm computational concave functions cone conjugate gradient conjugate gradient method Consider the following Consider the problem constraint qualification convergence convex function convex set defined denoted differentiable discussed dual problem duality equality constraints Example Exercise exists extreme point feasible region Figure following problem Fritz John Furthermore given global go to step gradient method Hence Hessian hyperplane inequality constraints iteration KKT conditions KKT point Lagrange multipliers Lagrangian dual Lagrangian multipliers Lemma line search linear programming linearly independent m x n matrix main step Mathematical Programming minimum nonempty Nonlinear Programming Note objective function objective value Operations Research optimal solution optimality conditions penalty function polyhedral set positive definite problem to minimize procedure pseudoconvex Quadratic Programming quasi-Newton Quasi-Newton Methods satisfies search directions second-order Section sequence Sherali Show simplex method strictly quasiconvex subgradient subject to Ax subject to g,(x suppose unconstrained variables vector zero