# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2019075

## An adaptively regularized sequential quadratic programming method for equality constrained optimization

 1 School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China 2 School of Mathematical Sciences, Soochow University, Suzhou, Jiangsu, China

* Corresponding author: Songqiang Qiu

Received  June 2018 Revised  March 2019 Published  July 2019

Fund Project: The first author is supported by the Fundamental Research Funds for the Central Universities 2014QNA62

In this paper, we devise an adaptively regularized SQP method for equality constrained optimization problem that is resilient to constraint degeneracy, with a relatively small departure from classical SQP method. The main feature of our method is an adaptively choice of regularization parameter, embedded in a trust-funnel-like algorithmic scheme. Unlike general regularized methods, which update regularization parameter after a regularized problem is approximately solved, our method updates the regularization parameter at each iteration according to the infeasibility measure and the promised improvements achieved by the trial step. The sequence of regularization parameters is not necessarily monotonically decreasing. The whole algorithm is globalized by a trust-funnel-like strategy, in which neither a penalty function nor a filter is needed. We present global and fast local convergence under weak assumptions. Preliminary numerical results on a collection of degenerate problems are reported, which are encouraging.

Citation: Songqiang Qiu, Zhongwen Chen. An adaptively regularized sequential quadratic programming method for equality constrained optimization. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019075
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##### References:
Performance compared to MINOS
Performance compared to LOQO
Compared to MINOS
 Use MINOS'Stopping rule. MINOS New Alg. Problem solved$<1500$ evals. 100 103 Robustness($<1500$ evals.) 95.24% 98.10% Average evals($<1500$ evals.) 84.04 67.5 Median evals($<1500$ evals.) 27 21
 Use MINOS'Stopping rule. MINOS New Alg. Problem solved$<1500$ evals. 100 103 Robustness($<1500$ evals.) 95.24% 98.10% Average evals($<1500$ evals.) 84.04 67.5 Median evals($<1500$ evals.) 27 21
Compared to LOQO.
 Use LOQO's Stopping rule. LOQO New Alg. Problem solved($<1500$ evals. 78 96 Robustness($<1500$ evals.) 74.30% 91.43% Average evals($<1500$ evals.) 26.6 62.1 Median evals($<1500$ evals.) 20 21
 Use LOQO's Stopping rule. LOQO New Alg. Problem solved($<1500$ evals. 78 96 Robustness($<1500$ evals.) 74.30% 91.43% Average evals($<1500$ evals.) 26.6 62.1 Median evals($<1500$ evals.) 20 21
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