Optimality in nonlinear programming: a feasible directions approach
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Characterizing Optimal Solutions
Some Computational Methods
4 other sections not shown
Algorithm 3.9 BEN-ISRAEL BEN-TAL binding constraints characterization Chebyshev solution computational constraint qualification contradicting convex cone convex program convex set denote direction of descent directions of constancy DNLP Dubovitskii-Milyutin equivalent Euler-Lagrange equation Exercises and Examples exists a vector faithfully convex functions feasible direction methods feasible point feasible set feasible solution fk(x Fritz John G Df(x GIRSANOV 72 Hence implies inconsistent index set inequality iteration John condition Kf(x Kuhn-Tucker condition Lemma lexicographic linear program linearly independent MANGASARIAN matrix MELP multipliers necessary condition non-negative nonascent nonempty nonlinear programming optimal solution Pareto minimum Pareto optimality posynomial primal problem Proof pseudoconvex quasiconvex quasiconvex functions quasiusable direction reduction condition relevant intervals satisfying scalars second-order conditions Section separation theorem set of binding Slater's condition subset ft sufficient condition sush thst TH(x Theorem 3.2 tions usable directions zero ZLOBEC