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Xiaojun Chen(xiaojun.chenpolyu.edu.hk) Abstract: This paper studies highorder evaluation complexity for partially separable convexlyconstrained optimization involving nonLipschitzian 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 qthorder stationary point in at most O(epsilon^{(p+1)/(pq+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 nonLipschitzian 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 partiallyseparable structure and nonLipschitzian group sparsity terms in the objective function may not affect the worstcase evaluation complexity order. Keywords: complexity theory, nonlinear optimization, nonLipschitz functions, partiallyseparable problems, group sparsity, isotropic model Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Category 2: Applications  Science and Engineering (DataMining ) Category 3: Applications  Science and Engineering (Statistics ) Citation: Download: [PDF] Entry Submitted: 02/27/2019 Modify/Update this entry  
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