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A cautious BFGS update for reduced Hessian SQP

机译:谨慎的BFGS更新,以减少黑森州的SQP

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In this paper, we introduce a cautious BFGS (CBFGS) update criterion in the reduced Hessian sequential quadratic programming (SQP) method. An attractive property of this update criterion is that the generated iterative matrices are always positive definite. Under mild conditions, we get the global convergence of the reduced Hessian SQP method. In particular, the second order sufficient condition is not necessary for the global convergence of the method. Furthermore, we show that if the second order sufficient condition holds at an accumulation point, then the reduced Hessian SQP method with CBFGS update reduces to the reduced Hessian SQP method with ordinary BFGS update. Consequently, the local behavior of the proposed method is the same as the reduced Hessian SQP method with BFGS update. The presented preliminary numerical experiments show the good performance of the method.
机译:在本文中,我们在简化的Hessian顺序二次规划(SQP)方法中引入了谨慎的BFGS(CBFGS)更新准则。该更新标准的一个吸引人的特性是,生成的迭代矩阵始终是正定的。在温和的条件下,我们得到了简化的Hessian SQP方法的全局收敛性。特别地,对于该方法的全局收敛,二阶充分条件不是必需的。此外,我们表明,如果二阶充分条件保持在一个累积点上,则具有CBFGS更新的简化Hessian SQP方法将还原为具有普通BFGS更新的简化Hessian SQP方法。因此,该方法的局部行为与具有BFGS更新的简化Hessian SQP方法相同。初步的数值实验表明了该方法的良好性能。

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