THE PENALTY FUNKCIONS METHOD AND OPTIMALITY CONDITONS
DOI:
https://doi.org/10.24234/scientific.v1i46.131Keywords:
Lipschitz functions, convex functions, Clark’s subdifferential, Lagrange coefficientsAbstract
The presented work is devoted to one of the most important areas of applied mathematics, namely mathematical programming.
The following general mathematical programming problem is considered where are Lipschitz, and is closed set.
The purpose of the work is to obtain optimality conditions for the problem posed using the method of penalty functions.
The obtained necessary conditions are expressed in the language of subdifferentials, which are a generalization of the method of indefinite Lagrange coefficients for nonsmooth optimization problems.
References
Hachatryan R.A. (2020). Metody optimizacii (Optimization methods), EGU, izd.
Dem'yanov V.F., Vasil'ev L.V. (1981). Nedifferenciruemaya optimizaciya (Non-differentiable optimization). M. Nauka.
Klark F. (1988). Optimizaciya i negladkij analiz (Optimization and non-smooth analysis). M. Nauka.
Pshenichnyj B.N. (1980). Vypuklyj analiz i ekstremal'nye zadachi (Convex analysis and extremal problems), M. Nauka.
Suharev A.G., Timohov A.G., Fedorov V.V. (1966). Kurs metodov optimizacii (Optimization Methods Course), M. Nauka.
Fedorov V.V. (1979). CHislennye metody maksimina (Numerical maximin methods). M. Nauka.
Clarke F. A mew approach to Langrange multipliers. Math. Oper., Res., 1. pp. 682-699.
Rockafellar R.T. (1979)., Clarke’s tangent cones and the boundaries of closed set, in , Nonlinear Analysis, Theory and Applications, pp.145-154.
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