A proof problem in nonlinear optimization

Asked Jun 15 '20 at 05:24

Active Jun 15 '20 at 05:27

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This is a problem in textbook Nonlinear Programming theory and algorithms, cuold anyone help me with the problem especially in the c. and d. part? Thank you in advance for your consideration.

edited Jun 15 '20 at 05:27

Harish Chandra Rajpoot

37,450

asked Jun 15 '20 at 05:24

李明轩

What ordering is being used on $\Bbb R^m$ to define $G_0$ and $G'$? I assume it must be lexicographical but that probably should be explicitly stated somewhere. – richard gayle Jun 15 '20 at 06:28
Assuming that the order means elementwise, then c. is not true. Take $A= \begin{bmatrix}0 \ 1 \end{bmatrix}$, then $G' = (-\infty,0]$ and $(G')^\circ = (-\infty,0)$, but $G_0 = \emptyset$. – copper.hat Jun 15 '20 at 06:31
What textbook is this from? – copper.hat Jun 15 '20 at 06:35
Nonlinear Programming theory and algorithms – 李明轩 Jun 15 '20 at 08:50

A proof problem in nonlinear optimization

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