The study of greedy approximation in the context convex optimization is becoming a promising research direction as algorithms are actively being employed to construct sparse minimizers for functions with respect given sets elements. In this paper we propose unified way analyzing certain kind greedy-type minimization on Banach spaces. Specifically, define class Weak Biorthogonal Greedy Algorithm...

We introduce a new quantum R\'enyi divergence $D^{\#}_{\alpha}$ for $\alpha \in (1,\infty)$ defined in terms of convex optimization program. This has several desirable computational and operational properties such as an efficient semidefinite programming representation states channels, chain rule property. An important property this is that its regularization equal to the sandwiched (also known...

This paper introduces a second-order differential inclusion for unconstrained convex optimization. In continuous level, solution existence in proper sense is obtained and exponential decay of novel Lyapunov function along with the trajectory derived as well. Then discrete based on numerical discretizations model, two inexact proximal point algorithms are proposed, some new convergence rates est...

In this study, a convex proximal point algorithm (CPPA) is considered for solving constrained non-convex problems, and new theoretical results are proposed. It proved that every cluster of CPPA stationary point, the initial key to global optimization. Several sufficient conditions selection provided find minimum. Motivated by these results, numerical experiments were conducted on quadratic prog...

Primal-dual algorithms, which are proposed to solve reformulated convex-concave saddle point problems, have been proven to be effective for solving a generic class of convex optimization problems, especially when the problems are ill-conditioned. However, the saddle point problem still lacks a distributed optimization framework where primal-dual algorithms can be employed. In this paper, we pro...