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the Huang family
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active constraints active set algorithm basic feasible solution basic variables column concave consider convex function convex set corresponding cost defined directions pr dual problem dual variables duality theorem elements equality constraints equations Example extreme point given gives global minimum Hence Hessian inequality Kuhn-Tucker conditions Lagrange multipliers Lagrangian linear programming matrix maximise maximum minima minimise f(x minimum point minimum value mixed strategy necessary conditions Newton Newton's method nonlinear objective function optimisation optimum orthogonal P2 playing payoff matrix penalty function pivot player point x1 positive definite primal problem minimise produces projection methods Proof prove quadratic function quadratic programming saddle point satisfy Section sequence Show simplex method slack variables solution set solve stationary point steepest descents Step strategies subject to c(x surplus variables symmetric Table tion unconstrained minimum vector xm+1 xr+1 zero