Geodesic
Lexicographic regularization and duality for improper linear programming problems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 279-291 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new approach to the optimal lexicographic correction of improper linear programming problems is proposed. The approach is based on the multistep regularization of the classical Lagrange function with respect to primal and dual variables simultaneously. The regularized function can be used as a basis for generating new duality schemes for problems of this kind. Theorems on the convergence and numerical stability of the method are presented, and an informal interpretation of the obtained generalized solution is given.
Keywords: linear programming, duality, improper problems, generalized solutions, regularization, penalty methods. 
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L. D. Popov; V. D. Skarin. Lexicographic regularization and duality for improper linear programming problems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 279-291. http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a27/

[1] Eremin I.I., “Dvoistvennost dlya nesobstvennykh zadach lineinogo i vypuklogo programmirovaniya”, Dokl. AN SSSR, 256:2 (1981), 272–276 | MR | Zbl

[2] Eremin I.I., Mazurov Vl.D., Astafev N.N., Nesobstvennye zadachi lineinogo i vypuklogo programmirovaniya, Nauka, M., 1983, 336 pp. | MR

[3] Eremin I.I., Dvoistvennost v lineinoi optimizatsii, Izd-vo UrO RAN, Ekaterinburg, 2001, 180 pp.

[4] Tikhonov A.N., Arsenin V.Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979, 285 pp. | MR

[5] Vasilev F.P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981, 400 pp. | MR

[6] Skarin V.D., “Ob odnom podkhode k analizu nesobstvennykh zadach lineinogo programmirovaniya”, Zhurn. vychisl. matematiki i mat. fiziki, 26:3 (1986), 439–448 | MR | Zbl

[7] Popov L.D., “Lineinaya korrektsiya nesobstvennykh minimaksnykh vypuklo-vognutykh zadach po maksiminnomu kriteriyu”, Zhurn. vychisl. matematiki i mat. fiziki, 26:9 (1986), 1100–1110 | MR

[8] Skarin V.D., “O metode regulyarizatsii dlya protivorechivykh zadach vypuklogo programmirovaniya”, Izv. vuzov. Matematika, 1995, no. 12, 81–88 | MR | Zbl

[9] Golshtein E.G., Teoriya dvoistvennosti v matematicheskom programmirovanii i ee prilozheniya, Nauka, M., 1971, 352 pp. | MR

[10] Eremin I.I., “O zadachakh posledovatelnogo programmirovaniya”, Sib. mat. zhurn., 14:1 (1973), 124–129

[11] Fedorov V.V., Chislennye metody maksimina, Nauka, M., 1979, 280 pp. | MR

[12] Guddat J., “Stability in convex quadratic programming”, Mathematische Operationsforschung und Statistik, 8 (1976), 223–245 | DOI | MR

[13] Dorn W.S., “Duality in quadratic programming”, Buart. Appl. Math., 1960, no. 18, 407–413 | MR | Zbl

[14] Hoffman A.J., “On approximate solutions of systems of linear inequalities”, J. Res. Nat. Bur. Standards, 49 (1952), 263–265 | DOI | MR