Summary
For a nonlinearly constrained convex extremal problem a general interior penalty method is given, that is Hadamard-stable and needs no compactness conditions for convergence. The rate of convergence of the values iso(t) fort→+0.
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References
Carroll, C.W.: The created response surface technique for optimizing nonlinear restrained systems. Operations Res.9, 169–184 (1961)
Fiacco, A.V., McCormick, G.P.: Nonlinear programming: Sequential unconstrained minimization techniques. New York: Wiley 1968
Frisch, K.R.: The logarithmic potential method of convex programming. Memorandum of May 13, 1955, University Institute of Economics, Oslo
Hartung, J.: Penalty-Methoden für Kontrollprobleme und Open-Loop-Differentialspiele. In: Optimization and optimal control (R. Bulirsch, W. Oettli, J. Stoer, eds.), Lecture Notes in Mathematics, Vol. 477, pp. 127–144. Berlin-Heidelberg-New York: Springer 1975
Hartung, J.: Zur Darstellung pseudoinverser Operatoren. Arch. Math.XXVIII, 200–208 (1977)
Holmes, R.B.: A course on optimization and best approximation. Lecture Notes in Mathematics, Vol. 257, Berlin-Heidelberg-New York: Springer 1972
Lasdon, L.S.: An efficient algorithm for minimizing barrier and penalty functions. Math. Programming2, 65–106 (1972)
Lootsma, F.A.: A survey of methods for solving constrained minimization problems via unconstrained minimization. In: Numerical methods for non-linear optimization (F.A. Lootsma, ed.), pp. 313–347. London-New York: Academic Press 1972
Sandblom, C.-L.: On the convergence of SUMT. Math. Programming6, 360–364 (1974)
Tichonow, A.N.: On the stability of the optimization problem. Zh. vychisl. Mat. mat. Fiz.6, 631–634 (1966)
Vignoli, A., Furi, M.: A characterization of well-posed minimum problems in a complete metric space. J. Optimization Theory Appl.5, 452–461 (1970)
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Hartung, J. A stable interior penalty method for convex extremal problems. Numer. Math. 29, 149–158 (1978). https://doi.org/10.1007/BF01390334
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DOI: https://doi.org/10.1007/BF01390334