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active constraint active inequality constraints affine space alternatives applied approximation assessed basic feasible solution basic variables Capital Investment column computational effort Consider convergence convex convex function cost current feasible solution cycle Decision Analysis decision maker decision problem defined descent direction determined discussed equality constraints equation fixed point go to step greedy heuristic guaranteed accuracy heuristic Hence Hessian heuristic algorithm integer interior point interval of uncertainty iteration Keeney knapsack problem knapsack's weight capacity label Lagrange multiplier line searches linear Markov Renewal process matrix MINIMIZE 6(x minimum Newton's method nonbasic variable nonlinear programming objective function optimization problem optimum objective value optimum solution positive definite positive number preferences programming problem quadratic ranking regenerative result satisfying search direction simplex solution obtained stage step length strategy subset termination theorem tion traveling salesman problem unconstrained minimization updating utility function utility independent vector vertex vertices