COMP 360 Lecture Notes - Lecture 10: Convex Set, Convex Combination, Slack Variable
27 Mar 2018
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Optimize a linear function that has been subject to linear inequalities. Constraints tell us what values the variables can take. Nash equilibrium - the 2 player game like rock paper scissors. Solve np hard problems using branch and cut. Production is limited by the scarce resources that are used as ingredients: corn, hop, barely, malt. The recipes for beer and ale are different. The way in which the profit is being maximized is unclear. We have variables x1 . xn - they must have non negative values. Claim: you can convert any lp into standard form. We convert inequalities to equalities by adding slack (s) variables to each equation. Each variable must have its own slack variable. Here sc sh and sm represent slack variables for corn, hops and malt respectively. This means that x+ and x- must be non negative however, their difference could be anything.
