A spectral conjugate gradient algorithm for vector optimization

This paper proposes a modified spectral conjugate gradient framework for solving unconstrained vector optimization problems. The method extends classical scalar techniques to the vector setting by incorporating a spectral scaling mechanism that preserves sufficient descent without requiring convexity assumptions or exact line searches. A central feature of the approach is a new spectral parameter, adapted from scalar optimization, which enables flexible integration with various conjugate direction updates. Within this framework, we introduce a specific variant based on a novel update rule for the conjugate parameter. Global convergence of both the general method and the proposed one is established under standard Wolfe-type conditions. Numerical experiments on benchmark problems confirm the effectiveness and computational competitiveness of the proposed strategies when compared with existing conjugate gradient schemes.