Mathematical Programming and Control Theory |
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algorithm applied assumed attain a minimum Banach spaces closed convex cone column conjugate Consider constraint set convergence convex cone convex function convex problem convex set Craven defined Denote derivatives DLFP DOC1 dual equivalent Exercise feasible finite Fréchet derivative Fréchet differentiable ƒ and g gradient Hence holds hypotheses implies inequality iteration L¹(I Lagrange multiplier Lagrangean LFEP linear constraints linear fractional program linear map linear program locally solvable mathematical programming matrix Maximize maximum minimization problem Minimize f(x Mond NFEP Nonlinear Programming norm objective function optimal control optimal control problem optimum P₁ positive definite positive semidefinite Proof q-equivalent quadratic programming Remark replaced sequence shows simplex method SLFP solution solved subspace sufficiently small t₁ theory u₁ variable vector space weak duality wh(a x₁ zero