2024/09/18 by Fatih S. Aktaş, Aktas, Fatih Selim, Mustafa Ç. Pı̆nar +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.2409.12343
openalex publication_date 2024/09/18 · openalex created_date 2024/10/27 · openalex updated_date 2026/07/28
This paper considers the minimization of a continuously differentiable function over a cardinality constraint. We focus on smooth and relatively smooth functions. These smoothness criteria result in new descent lemmas. Based on the new descent lemmas, novel optimality conditions and algorithms are developed, which extend the previously proposed hard-thresholding algorithms. We give a theoretical analysis of these algorithms and extend previous results on properties of iterative hard thresholding-like algorithms. In particular, we focus on the weighted ℓ2 norm, which requires efficient solution of convex subproblems. We apply our algorithms to compressed sensing problems to demonstrate the theoretical findings and the enhancements achieved through the proposed framework.