Lucchetti, Roberto On the continuity of the minima for a family of constrained optimization problems. (English) Zbl 0574.49017 Numer. Funct. Anal. Optimization 7, 349-362 (1985). The work deals with a parametrized family Py of constrained minimum problems \(Py=\min \{f(x,y):\) \(x\in Ky\}\). Here the function \(f: X\times Y\to {\mathbb{R}}\) and the multifunction \(K: Y\Rightarrow X\) are the data and X,Y are fixed Banach spaces. Working mainly in convexity it is shown how the property of Tykhonov well posedness of the (limit) problems allows to prove stability results usually achievable under compactness hypotheses on the images of the multifuction. Cited in 7 Documents MSC: 49K40 Sensitivity, stability, well-posedness 49J45 Methods involving semicontinuity and convergence; relaxation 90C48 Programming in abstract spaces 54C60 Set-valued maps in general topology Keywords:constrained minimum problems; multifunction; Tykhonov well posedness PDFBibTeX XMLCite \textit{R. Lucchetti}, Numer. Funct. Anal. Optim. 7, 349--362 (1985; Zbl 0574.49017) Full Text: DOI References: [1] Aubin, J.P. 1979. ”Mathematical methods of game and economic theory”. Amsterdam: North Holland. · Zbl 0452.90093 [2] Bednarczuc E., J. Math. Anal. Appl. 86 pp 309– (1982) · Zbl 0482.90080 · doi:10.1016/0022-247X(82)90225-6 [3] Berdysev V.I., Math. USSR - Sb. 32 pp 401– (1977) · Zbl 0396.90077 · doi:10.1070/SM1977v032n04ABEH002394 [4] Berge, C. 1963. ”Topological spaces”. New York: Macmillan Co. · Zbl 0114.38602 [5] Dantzig G., J. Math. Anal. Appl. 17 pp 519– (1967) · Zbl 0153.49201 · doi:10.1016/0022-247X(67)90139-4 [6] Dolecky S., J. Math. Anal. Appl. 69 pp 116– (1979) [7] Evans J.P., Oper. Res. 11 pp 107– (1973) [8] Furi M., J. Optim. Th. and Appl. 5 pp 225– (1970) · Zbl 0177.12904 · doi:10.1007/BF00927717 [9] Hager W., SIAM J. Control Optim. 17 pp 321– (1979) · Zbl 0426.90083 · doi:10.1137/0317026 [10] Hogan W., SIAM Rev. 15 pp 591– (1973) · Zbl 0256.90042 · doi:10.1137/1015073 [11] Laurent, F.J. 1972. ”Approximation et Optimization”. Paris: Hermann. [12] Lucchetti R., J. Math. Anal. Appl. 88 pp 204– (1982) · Zbl 0487.49013 · doi:10.1016/0022-247X(82)90187-1 [13] Lucchetti R., Boll. U.M.I. 1 pp 337– (1982) [14] Lucchetti R., Meth. of Oper. Res. 45 pp 113– (1983) [15] Lucchetti R., pubblicazioni 1st. Mat. Appl., Genoa 233 pp 1– (1983) [16] Robinson S., J. Math. Anal. Appl 45 pp 506– (1974) · Zbl 0291.90063 · doi:10.1016/0022-247X(74)90089-4 [17] Robinson S., SIAM J. Numer. Anal. 12 pp 754– (1975) · Zbl 0317.90035 · doi:10.1137/0712056 [18] Robinson S., SIAM J. Numer. Anal 13 pp 497– (1976) · Zbl 0347.90050 · doi:10.1137/0713043 [19] Zolezzi, T. ”On stability analysis in mathematical programming”. Edited by: A. V. Math. Programming Stud. (to appear) · Zbl 0624.49011 [20] Zolezzi T., Approximations and perturbations of minimum problems · Zbl 0403.49023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.