Transcription of Math 407 — Linear Optimization 1 Introduction
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Math 407 — Linear Optimization 1 Introduction
Math 407 Linear Optimization1 What is Optimization ?A mathematical Optimization problem is one in which some function is either maximized orminimized relative to a given set of alternatives. The function to be minimized or maximizedis called theobjective functionand the set of alternatives is called the feasible region (orconstraint region). In this course, the feasible region is always taken to be a subset ofRn(realn-dimensional space) and the objective function is a function further restrict the class of Optimization problems that we consider to Linear program-ming problems (or LPs).
2)=c 1x 1 +c 2x 2, the gradient of f is the same at every point in R2; rf(x 1,x 2)= c 1 c 2 . Recall from calculus that the gradient always points in the direction of increasing function values. Moreover, since the gradient is constant on the whole space, the level sets of f
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