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Operations research, linear programming, control theory, systems theory, optimal control, game theory
4
votes
1
answer
329
views
KKT conditions of problem with variational inequality constraint
I have an optimization problem with a variational inequality constraint:
$$
\begin{equation}
\begin{array}{ll}
\min_x & f(x) \\
\mathrm{s.t.} & g_i(x) \leq 0, \quad i=1,\ldots,m \\
& h_j(x) = 0, \qua …
0
votes
0
answers
156
views
Minimum circumscribed ellipsoid of $\mathcal H$-polytope
Given matrix $A \in \mathbb{R}^{m \times n}$ and vector $b \in \mathbb{R}^n$, consider the $\mathcal H$-polytope $P$ defined as follows
$$ P := \left\{ x \in \mathbb{R}^n : Ax \leq b \right\} $$
I wan …