A dual algorithm based on the smooth function proposed by Polyak (1988), for solving nonlinear programming problems with inequality constraints, is presented. The local convergence of the dual algorithm is established and the convergence rate is estimated. Numerical results given in tall paper show that this dual algorithm is effective for solving inequality constrained optimization problems.
A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.
In this paper, the uV-theory and P-differential calculus are employed to study second-order expansion of a class of D,C, functions and minimization problems. Under certain conditions, some properties of the u-Lagrangian, the second-order expansion of this class of functions along some trajectories are formulated. Some first and second order optimality conditions for the class of D,C, optimization problems are given.
