Nonlinear Programming: Analysis and Methods
Prentice-Hall, 1976 - 512 стор.
Classical optimization - unconstrained and equality constrained problems; Optimality conditions for constrained extrema; Convex sets and functions; Duality in nonlinear convex programming; Generalized convexity; Analysis of selected nonlinear programming problems; One-dimensional optimization; Multidimensional unconstrained optimization without derivative: empirical and conjugate direction methods; Second derivative, steepest descent and conjugate gradient methods; Variable metric algorithms; Penalty function methods; Solution of constrained problems by extensions of unconstrained optimization techniques; Approximation-type algorithms.
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algorithm applied approximation assume block called chapter choose chosen closed compute conjugate Consider constraints containing continuously convergence convex function convex programs convex set corresponding defined derivatives described differentiable discussed dual equality equations exact example exists extended feasible follows formula function evaluations function ƒ given Hence Hessian holds implies independent inequality interval iteration Lemma length linear linear program linearly Math matrix method minimization minimum move multipliers necessary Nonlinear Programming Note obtain optimal optimal solution penalty function positive definite preceding presented problem Proof prove quadratic function reader relation respect satisfying search directions sequence shown similar simplex method solution solving stage starting step strictly sufficient Suppose symmetric techniques termination Theorem tion unconstrained updating variable metric vector Vƒ(x