Abstract
This paper presents an acceleration of the optimal subgradient algorithm OSGA (Neumaier in Math Program 158(1–2):1–21, 2016) for solving structured convex optimization problems, where the objective function involves costly affine and cheap nonlinear terms. We combine OSGA with a multidimensional subspace search technique, which leads to a low-dimensional auxiliary problem that can be solved efficiently. Numerical results concerning some applications are reported. A software package implementing the new method is available.
Highlights
Over the past few decades, solving convex optimization with smooth or nonsmooth objectives has received much attention due to many applications in the fields of applied sciences and engineering, cf. [15,50]
This paper presents an acceleration of the optimal subgradient algorithm OSGA (Neumaier in Math Program 158(1–2):1–21, 2016) for solving structured convex optimization problems, where the objective function involves costly affine and cheap nonlinear terms
We combine OSGA with a multidimensional subspace search technique, which leads to a low-dimensional auxiliary problem that can be solved efficiently
Summary
Over the past few decades, solving convex optimization with smooth or nonsmooth objectives has received much attention due to many applications in the fields of applied sciences and engineering, cf. [15,50]. Similar to OSGA, OSGA-S needs to know about no global information except the strong convexity parameter μ (μ = 0 if it is not available), and it only requires the first-order information; the main advantage of OSGA-S is being able to handle problems with complex structure of the form (1) involving composition of several functions and linear operators. Such structured problems have received much attention due to increase of interest in using mixed regularization terms, e.g., [8]. We denote by fx and gx , the function value f (x) and the subgradient g at x ∈ C, respectively
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.
