# Questions tagged [semidefinite-programming]

Semidefinite programming can be regarded as an extension of linear programming. In a semidefinite program, the goal is to optimize a linear function over the intersection of the cone of positive semidefinite matrices with some affine space.

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### Relaxations for the spectral norm maximization problem

Optimizing the spectral norm of some positive semidefinite matrix $A(x) \in S^{n}$, w.r.t. a list of variables $x \in \mathbb{R}^d$ and semidefinite constraints is, in general, a nonconvex problem (...
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### Matrix norm minimization and matrix inner product

One of the famous problem in SDP is the matrix norm minimization (see S. Boyd, Convex Optimization, p. 170). Consider: \begin{equation}\label{eq:Lasse} \begin{aligned} &\min_{\mathbf{x}} & &...
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### Matrix inequality $a X \succeq arcsin(X)$ for some $a > 0$

Let $X \in S^{n}_{+}$ be a positive semi-definite matrix with $X_{ii} = 1$ for all $i \leq n$ (thus $X$ is a correlation matrix). Since $X$ is positive semi-definite, we have $|X_{ij}| \leq 1$ for any ...