Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

If I have a function i have to optimize subject to one constraint, are all feasible points automatically regular points since theres only one constraint?

share|improve this question

1 Answer 1

up vote 1 down vote accepted

No. Given $m$ constraints $g_1,g_2,\ldots,g_m:\mathbb R^n\to\mathbb R$, a point $x\in\mathbb R^n$ is called regular if the set of vectors $\{\nabla g_1(x),\nabla g_2(x),\ldots,\nabla g_m(x)\}$ is linearly independent. If there is only one constraint, the set is a singleton $\{\nabla g_1(x)\}$, but it may still not be linearly independent if $\nabla g_1(x)=0$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.