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首页> 外文期刊>Journal of Optimization Theory and Applications >Globally and Superlinearly Convergent QP-Free Algorithm for Nonlinear Constrained Optimization
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Globally and Superlinearly Convergent QP-Free Algorithm for Nonlinear Constrained Optimization

机译：全局和超线性收敛的无QP非线性约束优化算法

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摘要

A new, infeasible QP-free algorithm for nonlinear constrained optimization problems is proposed. The algorithm is based on a continuously differentiable exact penalty function and on active-set strategy. After a finite number of iterations, the algorithm requires only the solution of two linear systems at each iteration. We prove that the algorithm is globally convergent toward the KKT points and that, if the second-order sufficiency condition and the strict complementarity condition hold, then the rate of convergence is superlinear or even quadratic. MOreover, we incorporate two automatic adjustment rules for the choice of the penalty parameter and make use of an approximated direction as derivative of the merit function so that only first-order derivatives of the objective and constraint functions are used.
机译：针对非线性约束优化问题，提出了一种新的，不可行的无QP算法。该算法基于连续可微的精确罚函数和主动集策略。经过有限次迭代后，该算法每次迭代仅需要两个线性系统的解。我们证明了该算法在KKT点上是全局收敛的，并且，如果二阶充分条件和严格互补条件成立，则收敛速度是超线性的，甚至是二次的。 MOreover，我们结合了两个自动调整规则来选择惩罚参数，并利用近似方向作为优值函数的导数，从而仅使用目标函数和约束函数的一阶导数。

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