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Questions tagged [conic-optimization]

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1 vote
1 answer

Linearizing a quadratic constraint

I am working on a quadratic conic optimization problem, but I have discovered that it would be preferable if the quadratic constraint is linearly approximated. In other words, I need some way to make ...
1 vote
0 answers

Quadratic conic program duality

I am working on a problem relating to what is known as the "Good Deal risk measure" for production valuation in incomplete markets. I have created the following primal optimization problem, ...
0 votes
1 answer

Dual of second order cone programming with both equality and inequality constraints

How to derive the dual of a second order cone programming with both equality and inequality constraints? Here is the optimization problem I want to handle: $$ \begin{array}{rl}\min_{\mathbf{x},\mathbf{...
0 votes
0 answers

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 \...
4 votes
1 answer

Why does some solvers can only solve conic optimization problems?

Famous solvers like sedumi, sdpt3, mosek can solve conic optimization, but not more general convex optimization. Why? I know many convex problems can be formulated as conic, but still confused.
1 vote
1 answer

Questions on Mosek Fusion Power Cone example

Just trying to understand the example given in Mosek Fusion handbook as shown I'm not exactly sure how to convert 7.3 to 7.4 in terms of objective function. I understand the power cone $P_{3}^{0.2, 0....
-2 votes
1 answer

How can I model this Hyperbolic constraint?

In this problem, $\beta_u$, $w_{u,c}$ (a vector of complex elements), $x_u$ are optimization variables. Now, $||2\sqrt{\frac{\pi_u}{2}}\beta_u; h_{u,c}^{\rm H}w_{u,c}-\frac{1}{2\pi_u}x_u-1||_2\le h_{u,...
16 votes
3 answers

How to take the dual of a conic optimization problem?

Given a conic problem $$\min \{c^\top x \mid Ax \succeq_\mathit{C} b\}$$ for an arbitrary cone $C$, how can I construct the dual to the problem? Moreover, in Linear Programming one constructs the ...
11 votes
2 answers

Can SOCPs approximate better than LPs?

Are there any classes of NP-hard combinatorial optimization problems where Second order cone programs (SOCP) gives a better approximation than linear programs (LP)? I am looking for results in the ...