On the Primal Duty Geometry of Level Sets in Linear And Conic Optimization
On the Primal Duty Geometry of Level Sets in Linear And Conic Optimization
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To quickly assess the difficulty of the text, read a short excerpt:
1 we have Tc-e 5R is a i3-normal barrier for C, see [5]. Then F'{-) : intC* -> 5R, the conjugate function of F(-), is also a iJ-normal barrier for C", see [5] as well.
Let s° € intC* be given. The norm induced by the (^-normal barrier F(-) at . 5° is defined as follows: =o)v \\v\\, ^, o := ^vTH*[s^ where H*{s°) is the Hessian of F*{-) evaluated at s = s°. It then follows from Theorem 2. 1. 1 of [5] that B'{s\l) C C* and from Proposition 2. 3. 4 of [5] that ||s°||, _50 = \A?. Therefore under the... dual norm ||i;||, := ||v||t, sO we have Tc- > l/\/^.
3. 2 A Family of Norms on X for which tc* = 1 For every s° G intC*, there is a norm analogous to the Loo-norm for the nonnegative orthant, for which the associated min-width is tc — 1.
What to read after On the Primal Duty Geometry of Level Sets in Linear And Conic Optimization?
You can find similar books in the "Read Also" column, or choose other free books by Robert Michael Freund to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
1 we have Tc-e 5R is a i3-normal barrier for C, see [5]. Then F'{-) : intC* -> 5R, the conjugate function of F(-), is also a iJ-normal barrier for C", see [5] as well.
Let s° € intC* be given. The norm induced by the (^-normal barrier F(-) at . 5° is defined as follows: =o)v \\v\\, ^, o := ^vTH*[s^ where H*{s°) is the Hessian of F*{-) evaluated at s = s°. It then follows from Theorem 2. 1. 1 of [5] that B'{s\l) C C* and from Proposition 2. 3. 4 of [5] that ||s°||, _50 = \A?. Therefore under the... dual norm ||i;||, := ||v||t, sO we have Tc- > l/\/^.
3. 2 A Family of Norms on X for which tc* = 1 For every s° G intC*, there is a norm analogous to the Loo-norm for the nonnegative orthant, for which the associated min-width is tc — 1.
What to read after On the Primal Duty Geometry of Level Sets in Linear And Conic Optimization?
You can find similar books in the "Read Also" column, or choose other free books by Robert Michael Freund to read onlineMoreLess
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