Subgradient projection algorithms for constrained nonsmooth optimization. II: Nonlinear constraints. (English) Zbl 0817.90117
Summary: [For part I see the author and Y. Li, Numer. Math., Nanjing 12, No. 3, 270-283 (1990; Zbl 0735.65037).]
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 \(\varepsilon\)-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), \(\varepsilon\)-active constraints and \(\varepsilon\)-adjusted rules.
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 \(\varepsilon\)-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), \(\varepsilon\)-active constraints and \(\varepsilon\)-adjusted rules.
MSC:
90C30 | Nonlinear programming |
65K05 | Numerical mathematical programming methods |
49J52 | Nonsmooth analysis |
Keywords:
constrained nonsmooth optimization; subgradient projection algorithms; nonlinearly smooth constraints; \(\varepsilon\)-projection direction; Kuhn- Tucker conditions; \(\varepsilon\)-active constraints; \(\varepsilon\)- adjusted rulesCitations:
Zbl 0735.65037References:
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