解决向量优化问题的一种非单调投影梯度算法

A Nonmonotone Projected Gradient Algorithm for Solving Vector Optimization Problems

摘要: 本文引入一种新的算法：极大型投影梯度算法，它是将解决带约束向量优化问题的投影梯度算法和极大型非单调线搜索技术相结合的一种算法。下降方向通过由解决单目标规划的投影梯度算法推广到向量优化的投影梯度算法来得到，而在步长选择上采用经典的单调线搜索技术容易陷入局部收敛的困境，与非单调技术结合以后，可以摆脱这一困境。在合适的条件下，证明了算法的全局收敛和线性收敛性。

Abstract: This paper introduces a new algorithm: the max-type projected gradient algorithm, which combines the projected gradient algorithm for solving constrained vector optimization problems with the max-type nonmonotone line search technology. The Descent direction is obtained by extending the projection gradient algorithm for solving single objective programming to the projection gradient algorithm for vector optimization, while the classical monotone line search technology in step size selection is easy to fall into the dilemma of local convergence, which can be overcome by combining with nonmonotone technology. Under milder conditions, the global and linear convergences of the algorithm were demonstrated, and numerical experiments were conducted to verify its effective-ness.