2025/03/13 by Fernando García-Castaño, García-Castaño, Fernando, M. A. Melguizo Padial +1
Computer Science · Mathematics · #Optimization and Variational Analysis #Advanced Optimization Algorithms Research #Stochastic Gradient Optimization Techniques
paper · doi:10.48550/arxiv.2503.10193
This paper deals with ε-efficient and ε-properly efficient points with respect to a co-radiant set in vector optimization problems. In the first part of the paper, we establish a new nonlinear separation theorem for co-radiant sets in normed spaces. Subsequently, we obtain necessary and sufficient conditions, via scalarization, for both ε-efficient and ε-properly efficient points in a general framework, without requiring any assumptions on the co-radiant set or convexity conditions on the sets under consideration. Consequently, our results are applicable in a broader range of settings than those previously addressed in the literature.