AUTHORS: Javier F. Rosenblueth
Download as PDF
ABSTRACT: In nonlinear programming, the notion of quasinormality provides a constraint qualification which is in general weaker than that of normality, and it emerges naturally from an extended Lagrange multiplier rule. In this paper, we explain in detail its origin and some of its consequences in optimization theory for finite dimensional problems involving equality and inequality constraints, and provide a possible generalization to optimal control problems.
KEYWORDS: Lagrange multipliers, equality and inequality constraints, quasinormality, normality, optimal control
REFERENCES:
[1] J. A. Becerril, K. L. Cortez and J. F. Rosenblueth, Uniqueness of multipliers in optimal control: the missing piece, IMA J. Math. Control Inform. 2018, doi.org/10.1093/imamci/dny033
[2] A. Ben-Tal, Second-order and related extremality conditions in nonlinear programming, J. Optim. Theory Appl. 31, 1980, pp. 143–165.
[3] F. Clarke, Functional Analysis, Calculus of Variations and Optimal Control, Springer-Verlag, London 2013
[4] K. L. Cortez and J. F. Rosenblueth, Normality and uniqueness of Lagrange multipliers, Discrete Contin. Dyn. Syst. 38, 2018, pp. 3169– 3188.
[5] M. R. de Pinho and J. F. Rosenblueth, Mixed constraints in optimal control: an implicit function theorem approach, IMA J. Math. Control Inform. 24, 2017, pp. 197–218.
[6] G. Giorgi, A. Guerraggio and J. Thierfelder, Mathematics of Optimization: Smooth and Nonsmooth Case, Elsevier, Amsterdam 2004
[7] M. R. Hestenes, Calculus of Variations and Optimal Control Theory, John Wiley, New York 1966
[8] M. R. Hestenes, Optimization Theory, The Finite Dimensional Case, John Wiley, New York 1975
[9] J. Kyparisis, On uniqueness of Kuhn-Tucker multipliers in nonlinear programming, Math. Program. 32, 1985, pp. 242–246.
[10] E. J. McShane, The Lagrange Multiplier Rule, Amer. Math. Monthly, 80, 1973, pp. 922–925.
[11] G. Wachsmuth, On LICQ and the uniqueness of Lagrange multipliers, Oper. Res. Lett. 41, 2013, pp. 78–80.
