Questions tagged [sdp]
The sdp tag has no usage guidance.
5
questions
4
votes
1answer
87 views
Conditions required for strong duality to hold for SDPs
According to Wikipedia, strong duality holds when "the primal optimal objective and the dual optimal objective are equal."
What are the necessary conditions for strong duality to hold in ...
2
votes
1answer
86 views
Relationship between extreme points and optimal solutions of SDPs
Consider this to be our SDP problem:
Minimize $\langle C, X \rangle$ such that
$\langle A_i, X \rangle \ge b_i$ for all $i \in [m]$ and
$X \succcurlyeq 0$.
For SDPs, is there a relationship between ...
3
votes
0answers
124 views
SDP relaxation with greater-than and less-than inequalities at the same time
I am dealing with the following nonconvex fractional quadratic optimization problem
\begin{align}
& \min_{\boldsymbol{x}} && \max_{t \in \mathcal{T}} \frac{\boldsymbol{a}_t^T \boldsymbol{...
5
votes
1answer
114 views
Which solver solves PSD constrained convex non-linear problem
I have a problem with a vector variable $w \in \mathbb{R}^n$ and a symmetric matrix variable $V \in \mathbb{R^{n \times n}}$. I am solving a problem which is roughly like:
\begin{align}
\begin{array}{...
6
votes
0answers
51 views
Semi-definite Programming, non standard notation
The usual way to define a semi-definite program (SDP), e.g., as given in Boyd and Vandenberghe's convex optimization book, is:
$$
\begin{array}{cl}
\min & c^\top x \\
\mathrm{s.t.} & 0 \succeq ...
