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4 votes
0 answers
205 views

Basin of Attraction

I have a function $F$ which is defined as follows: $$ F(x) = \sum_{i=1}^N f(z_i^T x) $$ where ${z_i}$ are known $m \times 1$ vectors, $x$ is an $m \times 1$ vector, and for $t\in \mathbb{R}$, $f(t) = \...
1 vote
0 answers
100 views

Changing a nonlinear equality constraint into some conic inequality plus rank constraint

If we have a constraint optimization problem in which one of our constraint is $\prod\limits_{k = 1}^N {\left( {x - {a_k}} \right) = 0} $ . How could this nonlinear equality condition be changed into ...
4 votes
1 answer
2k views

lipschitz constant of a multivariate function

I have a function $f:\mathbb{R}^{50} \rightarrow \mathbb{R}$ and I need to compute the Lipschitz constant of $f$ to solve an optimization problem using a specific algorithm. Does any one have ...