lecture12 - Yinyu Ye MS&E Stanford MS&E211 Lecture...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #12 1 NonlinearOptimizationAlgorithmsIII YinyuYe DepartmentofManagementScienceandEngineering StanfordUniversity Stanford,CA94305,U.S.A. http://www.stanford.edu/˜yyye Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #12 2 Nonlinearlyconstrainedproblem ( NCOP ) minimize f ( x ) subjectto A x = b c ( x ) ≥ . Weassumethat A hasfullrankand f, c aredifferentiablefunctions,where c ( x )=( c 1 ( x ); ... ; c l ( x )) . TheKKTconditions: C ( x ) s = A x = b- A T y + ∇ f ( x ) T-∇ c ( x ) T s = ( c ( x ) , s ) ≥ , Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #12 3 where C ( x )= diag ( c ( x )) . Yinyu Ye, MS&E, Stanford MS&E211 Lecture Note #12 4 BarrierFunctionMethod ( BNCOP ) minimize f ( x )- μ ∑ l i =1 log c ( x ) i subjectto A x = b . TheKKTconditionofthebarrieredproblemis ∇ f ( x ) T- μ ∇ c ( x ) T C ( x )- 1 e- A T y = A x = b c ( x ) > , orusing s = μC ( x )- 1 e wehave C ( x ) s = μ e A x = b- A T y + ∇ f ( x ) T-∇ c ( x ) T s = . Yinyu Ye, MS&E, Stanford...
View Full Document

This note was uploaded on 06/16/2010 for the course MS&E 211 taught by Professor Yinyuye during the Fall '07 term at Stanford.

Page1 / 8

lecture12 - Yinyu Ye MS&E Stanford MS&E211 Lecture...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online