MITBoydintro

MITBoydintro - Convex Optimization Boyd &...

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Unformatted text preview: Convex Optimization Boyd & Vandenberghe 1. Introduction mathematical optimization least-squares and linear programming convex optimization example course goals and topics nonlinear optimization brief history of convex optimization 11 Mathematical optimization (mathematical) optimization problem minimize f ( x ) subject to f i ( x ) b i , i = 1 ,...,m x = ( x 1 ,...,x n ) : optimization variables f : R n R : objective function f i : R n R , i = 1 ,...,m : constraint functions optimal solution x has smallest value of f among all vectors that satisfy the constraints Introduction 12 Examples portfolio optimization variables: amounts invested in different assets constraints: budget, max./min. investment per asset, minimum return objective: overall risk or return variance device sizing in electronic circuits variables: device widths and lengths constraints: manufacturing limits, timing requirements, maximum area objective: power consumption data fitting variables: model parameters constraints: prior information, parameter limits objective: measure of misfit or prediction error Introduction 13 Solving optimization problems general optimization problem very difficult to solve methods involve some compromise, e.g. , very long computation time, or not always finding the solution exceptions: certain problem classes can be solved efficiently and reliably least-squares problems linear programming problems convex optimization problems Introduction 14 Least-squares minimize bardbl Ax b bardbl 2 2 solving least-squares problems...
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This note was uploaded on 01/04/2012 for the course CDS 212 taught by Professor Tarraf,d during the Fall '08 term at Caltech.

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MITBoydintro - Convex Optimization Boyd &...

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