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accumulation point Ai+k+l algorithm 2.1 algorithm for solving Armijo procedure assume assumption bounded and uniformly Chapter column vector Colville Computer conclude conditions for problem constrained optimization problems convergence theorem converges superlinearly convex quadratic corollary defined denoted Det(G dual Feasible Direction Algorithms Fritz-John gJ(xi Goldstein procedure gradient hence Hessian of f i+k+1 identity matrix inverse iteration Jacobian Kuhn-Tucker conditions Kuhn-Tucker point Lagrangian lemma linearly constrained linearly independent Lipschitz continuous Mangasarian Mathematics matrix G mean value theorem Method minimum n*n matrix Nonlinear Programming nonsingular NUMERICAL EXPERIENCE open set order of convergence primal feasible algorithm problem Q Proof quadratic rate quadratic termination quasi-Newton algorithm QUASI-NEWTON METHODS rate of convergence Rheinboldt satisfies solution stationary point stepsize procedure superlinear rate taking norms thesis Topkis tz v-z uniformly positive definite uniteigenvector update the matrix vergence Vf(x z e Rn