解无约束最优化问题的一个非单调的新的BFGS信赖域算法

给出了一个解无约束最优化问题的非单调的新的BFGS校正的信赖域算法．将非单调算法应用于解信赖域问题。前人已卓有成效．本文的关键之处就是提出了新的BFGS校正公式，此算法具有较好的性质。所给的BFGS校正的具有二次约束的信赖域子问题总保证校正矩阵是正定的。也即信赖域子问题是严格凸二次规划．在较少的假设条件下还结合相关理论证明了所提供的算法具有全局收敛性．

A New Nonmonotonic BFGS-Trust-Region Algorithm For Unconstrained Optimization

The paper proposes a nonmonotonic BFGS-trust-region algorithm for unconstrained optimization. By applying nonmonotonic algorithm to solve the problem of trust-region, people have acquired large achievements. The emphasis of the paper is to propose a new BFGS formula. The advantage of the algorithm is that the subproblem of trust-region method ensures that the update matrix is positive, that is, the subproblem is a strictly convex quadratic programming. In addition, by correlative theory we can prove the algorithm possesses global convergence under finite supposed conditions.