A Hybrid First-Order Method for Nonconvex $\ell_p$-ball Constrained Optimization

• DOI: 10.48550/arxiv.2104.04400
• Publication Date: 2021-01-01
• Authors: Xiangyu Yang; Hao Wang; Yichen Zhu; Xiao Wang
• Keywords: Smoothing; Ball (mathematics)

We investigate a class of nonconvex optimization problems characterized by feasible set consisting level-bounded regularizers, with continuously differentiable objective. propose novel hybrid approach to tackle such structured within first-order algorithmic framework combining the Frank-Wolfe method and gradient projection method. The step is amenable closed-form solution, while can be efficiently performed in reduced subspace. A notable characteristic our lies its independence from introducing smoothing parameters, enabling efficient solutions original nonsmooth problems. establish global convergence proposed algorithm show $O(1/\sqrt{k})$ rate terms optimality error for objectives under reasonable assumptions. Numerical experiments underscore practicality efficiency compared existing cutting-edge methods. Furthermore, we highlight how contributes advancement regularizer-constrained optimization.