In this paper, we propose a spectral Fletcher–Reeves conjugate gradient-like method for solving unconstrained bi-criteria minimization problems without using any technique of scalarization. We suggest an explicit formulae for computing a descent direction common to both criteria. The latter further verifies a sufficient descent property that does not depend on the line search nor on any convexity assumption. After proving the existence of a bi-criteria Armijo-type stepsize, global convergence of the proposed algorithm is established. Finally, some numerical results and comparisons with other methods are reported.

中文翻译：

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用于双标准优化的显式光谱 Fletcher-Reeves 共轭梯度法

在本文中，我们提出了一种类似谱弗莱彻-里夫斯共轭梯度的方法，用于在不使用任何标量化技术的情况下解决无约束双标准最小化问题。我们建议使用一个明确的公式来计算两个标准共同的下降方向。后者进一步验证了不依赖于线搜索也不依赖于任何凸性假设的充分下降属性。在证明双标准 Armijo 型步长的存在性之后，建立了所提出算法的全局收敛性。最后，报告了一些数值结果以及与其他方法的比较。