Transcription of Quadratic Functions, Optimization, and Quadratic Forms
{{id}} {{{paragraph}}}
Example: biology
Quadratic Functions, Optimization, and Quadratic Forms
Quadratic functions , Optimization, and Quadratic Fo r m s Robert M. Freund February, 2004 1 2004 Massachusetts Institute of 1 Quadratic Optimization A Quadratic optimization problem is an optimization problem of the form: T(QP) : minimize f (x):= 1 xT Qx + c x . Problems of the form QP are natural models that arise in a variety of settings. For example, consider the problem of approximately solving an over-determined linear system Ax = b, where A has more rows than columns. We might want to solve: (P1) : minimize Ax b x . Now notice that Ax b 2 = xT AT Ax 2bT Ax+bT b, and so this problem is equivalent to: (P1) : minimize xT AT Ax 2bT Ax + bT b x , which is in the format of QP.
A quadratic optimization problem is an optimization problem of the form: (QP) : minimize f (x):=1 xT Qx + c xT 2 s.t. x ∈ n. Problems of the form QP are natural models that arise in a variety of settings. For example, consider the problem of approximately solving an over-determined linear system Ax = b, where A has more rows than
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: