Proof of convergence for fmincon

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theOptimizer
theOptimizer 2023-1-23
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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回答（1 个）

Nayan
Nayan 2023-4-18
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

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