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.

中文翻译：

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一种无 Maratos 效应的等式约束优化的线搜索无惩罚 SQP 方法

针对非线性等式约束优化，提出了一种线搜索无惩罚的顺序二次规划方法。通常，可行方向用于最小化约束违反的度量，以处理线性化约束中的不一致性，而最优方向旨在提高最优性的度量。该方法的一个基本特征是，在每次迭代中都使用了作为可行方向和最优方向的某种凸组合的线搜索方向，从而充分降低了拉格朗日函数的值或约束违反的度量。在没有可行性恢复阶段的情况下分析了该方法的全局收敛性。在通常的假设下，该方法在没有二阶校正的情况下被证明是局部超线性收敛的，因此可以避免 Maratos 效应。几个例子的数值实验说明了该方法的局部行为。