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active constraint applied approximation basic feasible solution branch and bound column convergence convex convex function current feasible solution defined denote descent direction discussed ellipsoid algorithm equality constraints equations evaluated extreme point fixed charge flow amounts formulation go to step greedy heuristic Hence heuristic algorithm in-tree arcs inequality constraints input iteration knapsack problem labels Lagrange multiplier Lagrangian line searches linear programming lower bound Mathematical Programming minimization problem minimum MPSX NETG Newton's method node nonbasic variable Nonlinear Programming objective function objective value optimization problems optimum solution out-of-tree arc output parameter path polynomially bounded positive definite procedure programming problem quadratic quadratic programming satisfies simplex spanning tree specified stage step length subroutine subset terminate theorem tion traveling salesman problem UJ UJ unconstrained minimization updating upper bound zero