Subgradient projection algorithms for constrained nonsmooth optimization II: nonlinear constraints†

†This research was supported in part by the National Natural Science Foundation of China

Abstract

In this paper, a kind of subgradient projection algorithms is established for minimizing a locally Lipschitz continuous function subject to nonlinearly smooth constraints, which is based on the idea to get a feasible and strictly descent direction by combining the ∊-subgradient projection direction that attempts to satisfy the Kuhn-Tucker conditions with one corrected direction produced by a linear programming subproblem. The algorithm avoids the zigzagging phenomenon and converges to Kuhn-Tucker points, due to using the c.d.f. maps of Polak and Mayne (1985), ∊active constraints and ∊adjusted rules

Keywords:

• Constrained Nonsmooth Optimization
• Kuhn-Tucker Conditions
• Active Constraints
• Subgradient Projection Algorithm

†This research was supported in part by the National Natural Science Foundation of China

†This research was supported in part by the National Natural Science Foundation of China

Notes

†This research was supported in part by the National Natural Science Foundation of China