2012/10/10 by Zhaosong Lu, Lu, Zhaosong · 17 citations
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Artificial intelligence #Class (philosophy) #Computation (stat.CO) #Computer science #Convergence (economics) #Convex optimization #FOS: Computer and information sciences #FOS: Mathematics #Karush–Kuhn–Tucker conditions #Lipschitz continuity #Machine Learning (stat.ML) #Mathematical optimization #Mathematics #Nonlinear programming #Nonlinear system #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Regular polygon #Scheme (mathematics) #Sequence (biology) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1210.3039
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2012/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in which each iteration is obtained by solving a convex programming problem. Under some suitable assumptions, we establish that any accumulation point of the sequence generated by the methods is a KKT point of the SNLP problems. In addition, we propose a variant of the SCP method for SNLP in which nonmonotone scheme and ``local'' Lipschitz constants of the associated functions are used. A similar convergence result as mentioned above is established.