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Full-Text Articles in Physical Sciences and Mathematics
First-Order Algorithms For Nonlinear Structured Optimization, Miao Zhang
First-Order Algorithms For Nonlinear Structured Optimization, Miao Zhang
LSU Doctoral Dissertations
Nonlinear optimization is a critical branch in applied mathematics and has attracted wide attention due to its popularity in practical applications. In this work, we present two methods which use first-order information to solve two typical classes of nonlinear structured optimization problems.
For a class of unconstrained nonconvex composite optimization problems where the objective is the sum of a smooth but possibly nonconvex function and a convex but possibly nonsmooth function, we propose a unified proximal gradient method with extrapolation, which provides unified treatment to convex and nonconvex problems. The method achieves the best-known convergence rate for first-order methods when …