- Smoothing SQP Algorithm for Non-Lipschitz Optimization with Complexity Analysis Wei Bian(bianweilvse520163.com) Chen Xiaojun(maxjchenpolyu.edu.hk) Abstract: In this paper, we propose a smoothing sequential quadratic programming (SSQP) algorithm for solving a class of nonsmooth nonconvex, perhaps even non-Lipschitz minimization problems, which has wide applications in statistics and sparse reconstruction. At each step, the SSQP algorithm solves a strongly convex quadratic minimization problem with a diagonal Hessian matrix, which has a simple closed-form solution. The SSQP algorithm is easy to implement and has almost no time cost to solve the convex quadratic minimization subproblems. We show that the worst-case complexity of reaching an $\varepsilon$ scaled stationary point is $O(\varepsilon^{-2})$. Moreover, if the objective function is locally Lipschitz, the SSQP algorithm with a slightly modified updating scheme can obtain an $\varepsilon$ Clarke stationary point at most $O(\varepsilon^{-3})$ steps. Keywords: Smoothing SQP Algorithm, Non-Lipschitz Optimization, Complexity Analysis Category 1: Nonlinear Optimization (Unconstrained Optimization ) Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Category 3: Applications -- Science and Engineering (Statistics ) Citation: Department of Applied Mathematics, The Hong Kong Polytechnic University, February, 2012 Download: [PDF]Entry Submitted: 02/05/2012Entry Accepted: 02/05/2012Entry Last Modified: 02/05/2012Modify/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.