A line search penalty-free sequential quadratic programming method is proposed for nonlinear equality-constrained optimization. Generally, feasible directions are used to minimize the measurement of the constraint violation in order to deal with the inconsistency in the linearized constraints while optimal directions aim to improve the measure of optimality. A basic feature of the proposed method is that a line search direction that is some convex combination of a feasible direction and an optimal direction is utilized at each iteration, making either the value of the Lagrangian function or the measure of constraint violation sufficiently reduced. Global convergence of the method is analyzed without the feasibility restoration phase. Under the usual assumptions the method is shown to be superlinearly convergent locally without the second-order correction and hence the Maratos effect can be avoided. Numerical experiments on several examples illustrate the local behavior of the method. 

　　Publication: 

　　IMA Journal of Numerical Analysis, 2022, Volume 42, Issue 4, pp: 3771-3802. 

　　Author: 

　　Zhongwen Chen 

　　School of Mathematical Sciences, Soochow University, Suzhou 215006, China 

　　Yu-Hong Dai 

　　LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 

　　Email: dyh@lsec.cc.ac.cn 

　　Tauyou Zhang 

　　School of Mathematical Sciences, Soochow University, Suzhou 215006, China