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Questions tagged [semidefinite-programming]

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7 votes
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Time complexity of standard semidefinite programming solvers

I am interested in exact scaling of the ellipsoid method and interior point methods for solving SDPs. (I am not interested in algorithms like multiplicative weights updates method.)
• 121
6 votes
0 answers
515 views

Fastest exact algorithm for MAXCUT

Is the algorithm introduced in the following paper still the fastest exact algorithm for general MAXCUT problems? TIA Ryan Williams, A new algorithm for optimal $2$-constraint satisfaction and its ...
• 651
6 votes
0 answers
363 views

Approximating the diameter of a convex set defined by semidefinite constraints

A convex subset $C$ of $\mathbb{R}^{n^2}$ is given as the set of positive semidefinite $n\times n$ matrices whose coefficients fulfill some affine equations. Now, if you want to minimize a linear ...
4 votes
0 answers
106 views

Bounding a Solution of an SDP

It's common for convex optimization procedures to require a bounded region containing an optimal solution, either as input, like the initial ellipsoid of the ellipsoid method, or for run time bounds, ...
4 votes
0 answers
251 views

Testing emptiness property complexity in Sum of Squares Proof systems

Take the set $$\mathcal T=\{f_1(x_1,\dots,x_n)=\dots=f_m(x_1,\dots,x_n)=0, h_1(x_1,\dots,x_n)\geq a_1,\dots,h_t(x_1,\dots,x_n)\geq a_t\}$$ where h_1(x_1,\dots,x_n),\dots,h_t(x_1,\dots,x_n)\in\mathbb ...
• 539
3 votes
0 answers
77 views

Are there applications of Hyperbolic Programming other than Linear Programming and Semidefinite programming?

Title. It seems the most important special cases are LPs and SDPs. Are there other interesting special cases/applications for hyperbolic programming? (Apart from being super cool math on of itself) I ...
• 1,153
3 votes
0 answers
110 views

Can the Lasserre relaxation be defined over the reals?

If one wants to say minimize a function $f : \{-1,1\}^n \rightarrow \mathbb{R}$ on its domain then a degree$-d$ Lasserre relaxation of it would be to solve the problem of $\min \mathbb{E}_\mu [f(x)]$ ...
• 1,453
3 votes
0 answers
153 views

SOS and the small set expansion property

For what graphs do we know that their small set expansion property has a low degree SOS proof? Is this known to be true for say the complete graphs? A terminology issue about what is low degree" :...
• 1,453
3 votes
0 answers
89 views

First-order methods for solving SDP with geometric convergence or better

Is there any first-order method that can solve general SDP in a geometric (linear) rate? or super-geometric (super-linear) rate?
• 862
3 votes
0 answers
114 views

Quantum annealing or adiabatic quantum optimization with continuous optimization problems

How do quantum annealing or adiabatic quantum optimization deal with continuous optimization problems such as SDP?
• 131
3 votes
0 answers
225 views

The Quality of SDP relaxation on MaxCut

My question is: given a maxcut instance, if it costs too much to solve it to optimal practically but we can get an optimal solution of SDP relaxation quickly, can we assess the quality of this SDP ...
• 31
3 votes
0 answers
159 views

Gram matrix of Max-Cut relaxation

It seems that Goemans and Williamson give a unique representation for each graph of the semidefinite relaxation (elements $y_{ij}$ of Y). However, semidefinite programming may give the same maximum ...
• 573
2 votes
0 answers
188 views

• 1,153