Optimisation

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Author(s): F. A. Fischer, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IB Lecture Notes
Publisher: University of Cambridge
Year: 2015

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; optimization; control; optimal; optimisation; programming; linear programming; dynamic programming; lagrangian

Introduction and preliminaries
Constrained optimization
Review of unconstrained optimization
The method of Lagrange multipliers
Complementary Slackness
Shadow prices
Lagrange duality
Supporting hyperplanes and convexity
Solutions of linear programs
Linear programs
Basic solutions
Extreme points and optimal solutions
Linear programming duality
Simplex method
The simplex tableau
Using the Tableau
The two-phase simplex method
Non-cooperative games
Games and Solutions
The minimax theorem
Network problems
Definitions
Minimum-cost flow problem
The transportation problem
The maximum flow problem