# American Institute of Mathematical Sciences

• Previous Article
How's the performance of the optimized portfolios by safety-first rules: Theory with empirical comparisons
• JIMO Home
• This Issue
• Next Article
Characterizing robust weak sharp solution sets of convex optimization problems with uncertainty
November  2020, 16(6): 2675-2701. 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, 2020, 16 (6) : 2675-2701. doi: 10.3934/jimo.2019075
##### References:

show all references

##### 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
 [1] Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $L^2-$norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934/era.2020077 [2] Predrag S. Stanimirović, Branislav Ivanov, Haifeng Ma, Dijana Mosić. A survey of gradient methods for solving nonlinear optimization. Electronic Research Archive, 2020, 28 (4) : 1573-1624. doi: 10.3934/era.2020115 [3] Thierry Horsin, Mohamed Ali Jendoubi. On the convergence to equilibria of a sequence defined by an implicit scheme. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020465 [4] Parikshit Upadhyaya, Elias Jarlebring, Emanuel H. Rubensson. A density matrix approach to the convergence of the self-consistent field iteration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 99-115. doi: 10.3934/naco.2020018 [5] Touria Karite, Ali Boutoulout. Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020055 [6] Thomas Frenzel, Matthias Liero. Effective diffusion in thin structures via generalized gradient systems and EDP-convergence. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 395-425. doi: 10.3934/dcdss.2020345 [7] Yi-Long Luo, Yangjun Ma. Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 921-966. doi: 10.3934/dcds.2020304 [8] Sören Bartels, Jakob Keck. Adaptive time stepping in elastoplasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 71-88. doi: 10.3934/dcdss.2020323 [9] Andrew D. Lewis. Erratum for "nonholonomic and constrained variational mechanics". Journal of Geometric Mechanics, 2020, 12 (4) : 671-675. doi: 10.3934/jgm.2020033 [10] Kha Van Huynh, Barbara Kaltenbacher. Some application examples of minimization based formulations of inverse problems and their regularization. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020074 [11] Qiao Liu. Local rigidity of certain solvable group actions on tori. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 553-567. doi: 10.3934/dcds.2020269 [12] Li-Bin Liu, Ying Liang, Jian Zhang, Xiaobing Bao. A robust adaptive grid method for singularly perturbed Burger-Huxley equations. Electronic Research Archive, 2020, 28 (4) : 1439-1457. doi: 10.3934/era.2020076 [13] Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Klein-gordon equation. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020448 [14] Alberto Bressan, Sondre Tesdal Galtung. A 2-dimensional shape optimization problem for tree branches. Networks & Heterogeneous Media, 2020  doi: 10.3934/nhm.2020031 [15] Jia Cai, Guanglong Xu, Zhensheng Hu. Sketch-based image retrieval via CAT loss with elastic net regularization. Mathematical Foundations of Computing, 2020, 3 (4) : 219-227. doi: 10.3934/mfc.2020013 [16] Xuefei He, Kun Wang, Liwei Xu. Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium. Electronic Research Archive, 2020, 28 (4) : 1503-1528. doi: 10.3934/era.2020079 [17] Xin Guo, Lei Shi. Preface of the special issue on analysis in data science: Methods and applications. Mathematical Foundations of Computing, 2020, 3 (4) : i-ii. doi: 10.3934/mfc.2020026 [18] Shun Zhang, Jianlin Jiang, Su Zhang, Yibing Lv, Yuzhen Guo. ADMM-type methods for generalized multi-facility Weber problem. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020171 [19] Haiyu Liu, Rongmin Zhu, Yuxian Geng. Gorenstein global dimensions relative to balanced pairs. Electronic Research Archive, 2020, 28 (4) : 1563-1571. doi: 10.3934/era.2020082 [20] Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020345

2019 Impact Factor: 1.366