Abstract
A convex minimization problem in the form of the sum of two proper lower-semicontinuous convex functions has received much attention from the community of optimization due to its broad applications to many disciplines, such as machine learning, regression and classification problems, image and signal processing, compressed sensing and optimal control. Many methods have been proposed to solve such problems but most of them take advantage of Lipschitz continuous assumption on the derivative of one function from the sum of them. In this work, we introduce a new accelerated algorithm for solving the mentioned convex minimization problem by using a linesearch technique together with a viscosity inertial forward–backward algorithm (VIFBA). A strong convergence result of the proposed method is obtained under some control conditions. As applications, we apply our proposed method to solve regression and classification problems by using an extreme learning machine model. Moreover, we show that our proposed algorithm has more efficiency and better convergence behavior than some algorithms mentioned in the literature.
Highlights
In this work, we are dealing with a convex minimization problem, which can be formulated as min{ f ( x ) + g( x )}, x∈ H (1)where f, g : H → R ∪ {+∞} are proper, lower-semicontinuous convex functions and H is a Hilbert space
We are motivated to establish a novel accelerated algorithm for solving a convex minimization problem (1), which employs a linesearch technique introduced by Cruz and Nghia [20] together with viscosity inertial forward–backward algorithm (VIFBA) [19]
We prove its strong convergence theorem under weaker assumptions on the control conditions than that of VIFBA
Summary
We are dealing with a convex minimization problem, which can be formulated as min{ f ( x ) + g( x )}, x∈ H (1). One well-known method that has improved the convergence rate of (3) significantly is known as the fast iterative shrinkage-threshodling algorithm or FISTA. It was proposed by Beck and Teboulle [13], as seen in Algorithm 1. Most of the work related to a convex minimization problem assumes the L-Lipschitz continuity of O f This restriction can be relaxed using a linesearch technique. We are motivated to establish a novel accelerated algorithm for solving a convex minimization problem (1), which employs a linesearch technique introduced by Cruz and Nghia [20] together with VIFBA [19].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
