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algorithm alternative theorem applied assumed attain a minimum Banach spaces bounded Chapter closed convex cone column Consider constraint set continuous linear map continuously Frechet differentiable convergence convex cone convex function convex problem convex set Craven Denote DLFP dual dual space equivalent Exercise extreme points feasible G int gradient Hence holds hypotheses implies inequalities int5 iteration Lagrange multipliers Lagrangean LFEP linear constraints linear fractional program linear program locally solvable mathematical programming matrix Maximize maximum minimization problem Mond Newton's method NFEP Nonlinear Programming objective function optimal control optimal control problem optimum positive definite Proof quadratic programming Remark replaced S C Y sequence shows simplex method SLFP solution subspace sufficiently small theory unconstrained minimization uniform norm variables vector space weak duality zero