Proof of convergence for fmincon

Question

theOptimizer 2023-1-23

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https://ww2.mathworks.cn/matlabcentral/answers/1898960-proof-of-convergence-for-fmincon

回答： Nayan 2023-4-18

Hi, I would like to formulate a convergence proof for the fmincon solver (interior-point-method) and my global nonlinear problem.

My problem is definitely bounded from below and I assume that my starting point is inside the basin of attraction (of course, I cannot prove this). I also assume that my problem is smooth.

In the description of the algorithm, several papers are cited and I am not sure which of the algorithms is implemented in Matlab.

It would be helpful if I could find the exact paper used to implement it (ideally with a proof of convergence) or a general proof describing what assumptions must hold for the interior point method to converge.

Many greetings and thanks in advance

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Answer 1

Nayan 2023-4-18

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Hi theOptimizer,

MATLAB's “fmincon()” function implements several algorithms. MATLAB will choose automatically the best possible algorithm. In most cases it will be an interior-point algorithm.

I would suggest you go through the following link, which explains the "fmincon()” Interior Point Algorithm" in detail.

Link: Constrained Nonlinear Optimization Algorithms - MATLAB & Simulink (mathworks.com)

Hope this helps!

Cheers

Nayan