Linear and nonlinear programming
Linear programming; Further computational algorithms and topics in linear programming; Linear duality theory; Topics in linear programming and statistics; Saddle point optimality criteria of nonlinear programming problems; Saddle point characterization and quadratic programming; Geometric programming.
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Further Computational Algorithms and Topics in Linear Programming
Linear Duality Theory
Topics in Linear Programming and Statistics
7 other sections not shown
artificial variables associated Assume basic solution basic variable Chapter coefficients column components consider the following Consider the problem constraints convex cone convex function convex set cost defined denotes determine dual problem duality enter the basis equations equivalent Example exists extreme point feasible region feasible solution final tableau following problem geometric programming Hence hyperplane implies inequality infeasible iteration Kuhn-Tucker conditions Lagrange multipliers Lagrangian Lagrangian function leaves the basis linear programming model linear programming problem lower bound Math matrix maximize c'x subject maximum MPSX multiply negative nonlinear programming nonnegative objective function obtain optimal solution orthant positive posynomial primal problem problem minimize procedure profit Proof quadratic programming resource vector restrictions Row0 saddle point solution saddle value problem satisfies simplex algorithm slack variable solution of Problem solves Problem subject to Ax surplus variables Theorem 7.1 tion unit upper bound x'Dx x2 subject zero