Dear Manish Kumar Sahu

These articles might be an asset, have a look:

1. https://openreview.net/forum?id=EQtwFlmq7mx

2. https://arxiv.org/abs/2004.01977

Kind Regards

Qamar Ul Islam

Dear Manish Kumar Sahu,

I suggest you to see links and attached files on topic.

https://era.library.ualberta.ca/items/976b918d-5965-4bb3-b3fd-dc8edf943276/view/7d892d9a-6489-4140-8b6c-ab5a3cac1e1e/zhu_rui_201812_PhD.pdf

https://researchportal.be/en/project/efficient-algorithms-large-scale-minimax-problems

https://www.hindawi.com/journals/jmath/2021/5540262/

Article An efficient algorithm for non-convex sparse optimization

Preprint Effcient Projection Onto the Nonconvex $\ell_p$-ball

Preprint Fast and Stable Nonconvex Constrained Distributed Optimizati...

Chapter Numerical Methods for Large-Scale Nonsmooth Optimization

Best regards

Thank you @Qaman UI Islam and @Mohamed-Mourad Lafifi

Interior point methods (https://en.wikipedia.org/wiki/Interior-point_method) are generally superior to active-set methods (https://en.wikipedia.org/wiki/Active-set_method) for solving large-scale problems.

You usually end up solving a convexified equality-constrained problem, that is a system of nonlinear equations. That's the most favorable case.

Among active-set methods, SLQP (https://en.wikipedia.org/wiki/Sequential_linear-quadratic_programming) is of particular interest. It also forms an equality-constrained quadratic problem (the favorable case) after it approximated the set of active inequality constraints by solving a linear problem.