https://github.com/hurak/generalizedeigenvalueminimization.jl

Minimization of the (maximum) generalized eigenvalue under linear matrix inequality (LMI) constraints.
https://github.com/hurak/generalizedeigenvalueminimization.jl

Last synced: 2 months ago
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Minimization of the (maximum) generalized eigenvalue under linear matrix inequality (LMI) constraints.

• Host: GitHub
• URL: https://github.com/hurak/generalizedeigenvalueminimization.jl
• Owner: hurak
• License: mit
• Created: 2021-07-12T10:51:05.000Z (almost 4 years ago)
• Default Branch: master
• Last Pushed: 2021-09-27T10:50:08.000Z (over 3 years ago)
• Last Synced: 2025-02-08T04:26:43.890Z (4 months ago)
• Language: Julia
• Size: 106 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# GeneralizedEigenvalueMinimization.jl

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An (experimental) Julia package for solving the following optimization problem

```math

minimize                λ

over x∈Rⁿ, λ∈R

subject to              λB(x)-A(x)≻0

                        B(x)≻0

                        C(x)≻0

where A(), B() and C() are affine functions of x, and the interpretation of the inequalities is that the matrices on the left are positive definite.

```

The package implements (or plans to implement) a few solution methods:

1. Bracketing over `λ`: for a fixed `λ` the problem reduces to eigenvalue minimization problem, for which efficient algorithms exist.

2. The *method of centers for minimizing generalized eigenvalues* described in Boyd, Stephen, and Laurent El Ghaoui. “Method of Centers for Minimizing Generalized Eigenvalues.” Linear Algebra and Its Applications 188–189 (July 1, 1993): 63–111. https://doi.org/10.1016/0024-3795(93)90465-Z. Also available online at https://web.stanford.edu/~boyd/papers/gevc.html. The method is also implemented in Robust Control Toolbox for Matlab as [gevp](https://www.mathworks.com/help/robust/ref/gevp.html) function (internally relying on LMI Toolbox).