- High-Order Evaluation Complexity for Convexly-Constrained Optimization with Non-Lipschitzian Group Sparsity Terms Xiaojun Chen(xiaojun.chenpolyu.edu.hk) Philippe L. Toint(philippe.tointunamur.be) Abstract: This paper studies high-order evaluation complexity for partially separable convexly-constrained optimization involving non-Lipschitzian group sparsity terms in a nonconvex objective function. We propose a partially separable adaptive regularization algorithm using a $p$-th order Taylor model and show that the algorithm can produce an (epsilon,delta)-approximate q-th-order stationary point in at most O(epsilon^{-(p+1)/(p-q+1)}) evaluations of the objective function and its first p derivatives (whenever they exist) Our model uses the underlying rotational symmetry of the Euclidean norm function to build a Lipschitzian approximation for the non-Lipschitzian group sparsity terms, which are defined by the group \ell_2-\ell_a norm with a in (0,1). The new result shows that the partially-separable structure and non-Lipschitzian group sparsity terms in the objective function may not affect the worst-case evaluation complexity order. Keywords: complexity theory, nonlinear optimization, non-Lipschitz functions, partially-separable problems, group sparsity, isotropic model Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 2: Applications -- Science and Engineering (Data-Mining ) Category 3: Applications -- Science and Engineering (Statistics ) Citation: Download: [PDF]Entry Submitted: 02/27/2019Entry Accepted: 02/27/2019Entry Last Modified: 02/27/2019Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.