# Questions tagged [semidefinite-programming]

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### How to check optimality of conic optimization problem

I'm trying to solve this problem, but I'm not sure if it is possible to check the optimality of this problem. \min_{K,L} \quad Tr(L^\top L)\qquad\\ \text{s.t.} \quad K^\top L = A^\top Q\\ \qquad \...
1 vote
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### interior point computational complexity for SDP

I am trying to get the complexity of the SDP problem for my specific problem, but I’m facing some problems. I found in the literature that the complexity of the SDP problem for an interior point per ...
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1 vote
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### Distributionally Robust Stochastic Programming - Help with derivation

I've been working through this book on robust optimization of electric energy systems, and in particular chapter 4 on distributionally robust optimization. In following the derivation of section 4.2.1....
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### Augmented Lagrangian Function for Semidefinite Programming Problems

I am currently reading the paper "Alternating direction augmented Lagrangian methods for semidefinite programming" and was wondering about how one comes up with the Augmented Lagrangian ...
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### Adequate SDP solvers for large problem instances

I have previously used MOSEK for all my SDP needs. Recently, though, I am having a hard time trying to solve some large problems, due to lack of memory. In similar questions around the forum, SCS has ...
• 49
323 views

### Solver for nonlinear semidefinite optimization

Totally new to optimization. Is there an easy-to-use solver, package, (free) software for solving nonlinear semidefinite optimization problems?
• 129
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### Non-symmetric Positive Definite/Semidefinite Matrix in Quadratic Program

A necessary condition in any quadratic programming to be convex is the matrix $\mathbf{Q}$ in the formulation $x^\intercal \mathbf{Q}x$ to be positive definite or positive semidefinite. Positive ...
• 245
105 views

### Is this semidefinite constraint in fact pointless?

On Wikipedia, I encountered a statement that the semidefinite relaxation of a quadratically constrained quadratic program can be solved more efficiently (using only LP) in the case that no variable is ...
• 201