Nonlinear Programming: Analysis and Methods
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This graduate-level text requires no advanced mathematical background beyond elementary calculus, linear algebra, and real analysis. 1976 edition. 58 figures. 7 tables.
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approximation assume Avriel chapter compute concave functions conjugate directions conjugate functions constrained problems constraint qualification convergence convex programs convex set defined derivatives descent method dual program duality equations example exists feasible set finite follows func function evaluations geometric programming given global minimum Hence Hessian matrix hyperplane inequality iteration Kuhn-Tucker Lagrange multipliers Lagrangian Lemma Let f line searches linear program linearly independent local minimum Math Mathematical Programming necessary conditions Newton's method nonempty Nonlinear Programming nonnegative objective function obtain optimal solution penalty function penalty function methods points x1 positive definite positive number primal programming problem Proof proper convex function pseudoconvex quadratic function quadratic program quadratic termination quasiconvex function reader real function satisfying search directions solving steepest descent step length sufficient conditions Suppose symmetric Theorem theory tion unconstrained minimization unconstrained optimization updating formula variable metric algorithms vector