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A sequential quadratic programming algorithm with non-monotone line search. (English) Zbl 1154.65046

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.

MSC:

65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C55 Methods of successive quadratic programming type

Software:

NLPQLP; CUTEr; MISQP; QL
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