Optimization Under Constraints: Theory and Applications of Nonlinear ProgrammingFirst thoughts on maximization; Constrained maximization and lagrangian methods; The strong lagrangian principle: convexity; Linear programming; Some particular linear problems; Some problems with linear constraints; Nonlinear constraints, and stochastic effects; Numerical methods; Vector maximization problems. |
Contents
First Thoughts on Maximization | 1 |
Constrained Maximization and Lagrangian Methods | 18 |
Convexity | 36 |
Copyright | |
9 other sections not shown
Common terms and phrases
allocation problem amount argument assertion assumption attained basic bound boundary point characterization chosen co-ordinate coefficients concave concave function cone constant constrained maximization problem convex cone convex hull convex set corresponding cost denoted derivatives determined direction distribution dual problem efficient points elements equality constraints example Exercise exists expression extractor fact feasible Figure finite flow follows function f(x given graph implies inequality interior interpretation interval inversion Lagrangian form Lagrangian methods Lagrangian multipliers Lagrangian theory linear programming load matrix maximizing f(x min-max theorem node non-negative scalar nonlinear optimal player Po(b positive prescribed probability problem of Section randomized solution recursion relation respect saddle-point satisfy sequence Show simplex method stationary point strategy strong Lagrangian principle structure supporting hyperplane supporting hyperplane theorem Suppose supremum tion u₁ utility valid variables variation vector x-values x₁ zero