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A sequential quadratic programming (SQP) algorithm is designed for nonsmoothoptimization problems with upper-C^2 objective functions. Upper-C^2 functionsare locally equivalent to difference-of-convex (DC) functions with smoothconvex parts. They arise naturally in many applications such as certain classesof solutions to parametric optimization problems, e.g., recourse of stochasticprogramming, and projection onto closed sets. The proposed algorithm conductsline search and adopts an exact penalty merit function. The potentialinconsistency due to the linearization of constraints are addressed throughrelaxation, similar to that of Sl_1QP. We show that the algorithm is globallyconvergent under reasonable assumptions. Moreover, we study the localconvergence behavior of the algorithm under additional assumptions ofKurdyka-{\L}ojasiewicz (KL) properties, which have been applied to manynonsmooth optimization problems. Due to the nonconvex nature of the problems, aspecial potential function is used to analyze local convergence. We show thatunder acceptable assumptions, upper bounds on local convergence can be proven.Additionally, we show that for a large number of optimization problems withupper-C^2 objectives, their corresponding potential functions are indeed KLfunctions. Numerical experiment is performed with a power grid optimizationproblem that is consistent with the assumptions and analysis in this paper.

Local convergence of a sequential quadratic programming method for a class of nonsmooth nonconvex objectives