MSC:
49A27,
49J27,
49J45,
49K40,
49M30,
54D35,
54E05,
65K10,
90C48,
90C99 | MR 1042847 | Zbl 0714.49006

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constrained optimization; level sets; minimizing sequences; penalty functions; compactifications; problems with tolerance

References:

[1] Á. Császár: **General Topology**. Akademiai Kiadó, Budapest, 1978. MR 1796928

[2] A. V. Efremovich: **The geometry of proximity**. (in Russian). Mat. Sbornik 31 (73) (1952), 189-200. MR 0055659

[3] E. K. Golshtein: **Duality Theory in Mathematical Programming and Its Applications**. (in Russian). Nauka, Moscow, 1971. MR 0322531

[4] D. A. Molodcov: **Stability and regularization of principles of optimality**. (in Russian). Zurnal vycisl. mat. i mat. fiziki 20 (1980), 1117-1129. MR 0593496

[5] D. A. Molodcov: **Stability of Principles of Optimality**. (in Russian). Nauka, Moscow, 1987.

[6] L. Nachbin: **Topology and Order**. D. van Nostrand Соmр., Princeton, 1965. MR 0219042 | Zbl 0131.37903

[7] S. A. Naimpally B. D. Warrack: **Proximity Spaces**. Cambridge Univ. Press, Cambridge, 1970. MR 0278261

[8] E. Polak Y. Y. Wardi: **A study of minizing sequences**. SIAM J. Control Optim. 22 (1984), 599-609. DOI 10.1137/0322036 | MR 0747971

[9] T. Roubíček: **A generalized solution of a nonconvex minimization problem and its stability**. Kybernetika 22 (1986), 289-298. MR 0868022

[10] T. Roubíček: **Generalized solutions of constrained optimization problems**. SIAM J. Control Optim. 24 (1986), 951-960. DOI 10.1137/0324056 | MR 0854064

[11] T. Roubíček: **Stable extensions of constrained optimization problems**. J. Math. Anal. Appl. 141 (1989), 520-135, DOI 10.1016/0022-247X(89)90210-2 | MR 1004588

[12] Yu. M. Smirnov: **On proximity spaces**. (in Russian). Mat. Sbornik 31 (73) (1952), 534-574. MR 0055661 | Zbl 0152.20904

[13] J. Warga: **Optimal Control of Differential and Functional Equations**. Academic press, New York, 1972. MR 0372708 | Zbl 0253.49001