Transcription of Chapter 3 Quadratic Programming
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Chapter 3 Quadratic Programming
Optimization I; Chapter 356 Chapter 3 Quadratic Constrained Quadratic Programming problemsA special case of the NLP arises when the objective functionalfis quadraticand the constraintsh, gare linear inx lRn. Such an NLP is called a QuadraticProgramming (QP) problem. Its general form isminimizef(x) :=12xTBx xTb( )overx lRnsubject toA1x=c( )A2x d ,( )whereB lRn nis symmetric,A1 lRm n, A2 lRp n, andb lRn, c lRm, d we shall see in this Chapter , the QP ( )-( ) can be solved iterativelyby active set strategies or interior point methods where each iteration requiresthe solution of an equality constrained QP Equality constrained Quadratic programmingIf only equality constraints are imposed, the QP ( )-( ) reduces tominimizef(x) :=12xTBx xTb( )overx lRnsubject toAx=c ,( )whereA lRm n, m n.
Optimization I; Chapter 3 56 Chapter 3 Quadratic Programming 3.1 Constrained quadratic programming problems A special case of the NLP arises when the objective functional f is quadratic and the constraints h;g are linear in x 2 lRn. Such an NLP is called a Quadratic Programming (QP) problem. Its general form is minimize f(x) := 1 2 xTBx ¡ xTb ...
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