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Nonlinear Unconstrained Optimization
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algorithm applied approximation assume Banach space Branch and Bound Chapter coefficients column components computation conjugate consider constrained optimization constraints continuously differentiable convex function convex set corresponds cutting plane cutting-plane defined denote derivatives dimension direction dual function dual problem dual variables duality dynamic programming equation equivalent example exists feasible finite number global convergence Gomory gradient method graph hence Hilbert space inequality integer programming integral solution iterations knapsack problem Kuhn and Tucker Lagrange function Lagrangean relaxation linear programme lower bound Mathematical Programming matrix Minimize minimum Minoux multi-commodity flow multipliers Newton's method Nonlinear Programming obtained optimal solution optimal value optimization problems optimum possible primal programming problems Proof quadratic quasi-Newton methods rate of convergence reduced saddle-point satisfies sequence shortest path problem Simplex method solving step subgradient subgradient method subset Theorem theory traveling salesman problem unconstrained vector space vertex vertices