Transcription of Chapter 12 Quadratic Optimization Problems
{{id}} {{{paragraph}}}
Example: biology
Chapter 12 Quadratic Optimization Problems
Chapter 12 Quadratic Optimization Quadratic Optimization : The Positive DefiniteCaseIn this Chapter , we consider two classes of Quadratic opti-mization Problems that appear frequently in engineeringand in computer science (especially in computer vision) (x)=12x Ax+x bover allx Rn, (x)=12x Ax+x bover the unit 12. Quadratic Optimization PROBLEMSIn both cases,Ais a symmetric matrix. We also seeknecessary and sufficient conditions forfto have a Problems in physics and engineering can be statedas theminimization of some energy function,withorwithout , it is a fundamental principle of mechanics thatnature acts so as to minimize , if a physical system is in a stable state ofequilibrium, then the energy in that state should be simplest kind of energy function is a Quadratic Quadratic Optimization .
12.1. QUADRATIC OPTIMIZATION: THE POSITIVE DEFINITE CASE 455 Thus, when the energy function P(x)ofasystemisgiven by a quadratic function P(x)= 1 2 xAx−xb, where A is symmetric positive definite, finding the global minimum of P(x) is equivalent to solving the linear system Ax = b. Sometimes, it is useful to recast a linear problem Ax = b
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: