Dai, Yu-Hong; Schittkowski, Klaus A sequential quadratic programming algorithm with non-monotone line search. (English) Zbl 1154.65046 Pac. J. Optim. 4, No. 2, 335-351 (2008). The following nonlinear constraint minimization problem is considered: \[ \text{minimize }f(x)\text{ subject to }g_j(x)= 0,\;j= 1,\dots, p,\;g_j(x)\geq 0,\;j= p+1,\dots, m, \]where \(x\in\mathbb{R}^n\) and \(f(x)\), \(g_j(x)\) are continuously differentiable on \(\mathbb{R}^n\). The authors point out that sequential quadratic programming methods stabilized by a monotone line search procedure are quite sensitive in case of round-off and approximation errors, which may occur in function and gradient values. The aim of the paper is to propose a non-monotone line search. The proposed method allows the acceptance of a step length even with an increased merit function value and reduces in this way the number of false terminations. The stability of the algorithm proposed is documented on a set of 306 test problems of collections quoted in the list of literature. The authors recommend monotone line searches as long as they terminate successfully and apply the non-monotonic algorithm if the monotone line search fails. Reviewer: Karel Zimmermann (Praha) Cited in 1 ReviewCited in 5 Documents MSC: 65K05 Numerical mathematical programming methods 90C26 Nonconvex programming, global optimization 90C30 Nonlinear programming 90C55 Methods of successive quadratic programming type Keywords:sequential quadratic programming; nonlinear programming; non-monotone line search; numerical examples; nonlinear constraint minimization problem; stability; algorithm Software:NLPQLP; CUTEr; MISQP; QL PDFBibTeX XMLCite \textit{Y.-H. Dai} and \textit{K. Schittkowski}, Pac. J. Optim. 4, No. 2, 335--351 (2008; Zbl 1154.65046)