2018/05/30 by Yen-Huan Li, Carlos A. Riofrío, Li, Yen-Huan +3 · 1 citation
Computer Science · Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Quantum Information and Cryptography #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1805.12232
openalex publication_date 2018/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Existing convergence guarantees for the mirror descent algorithm require the objective function to have a bounded gradient or be smooth relative to a Legendre function. The bounded gradient and relative smoothness conditions, however, may not hold in important applications, such as quantum state tomography and portfolio selection. In this paper, we propose a local version of the relative smoothness condition as a generalization of its existing global version, and prove that under this local relative smoothness condition, the mirror descent algorithm with Armijo line search always converges. Numerical results showed that, therefore, the mirror descent algorithm with Armijo line search was the fastest guaranteed-to-converge algorithm for quantum state tomography, empirically on real data-sets.