×

Algorithmic solution of two parametric optimization problems of a set of complete combinations. (English. Russian original) Zbl 0985.90086

Cybern. Syst. Anal. 35, No. 6, 981-986 (1999); translation from Kibern. Sist. Anal. 1999, No. 6, 160-165 (1999).
Summary: Algorithmic solutions of parametric problems of two types (with a parameter in the objective function and with a parameter in the system of constraints) are considered in a Euclidean combinatorial set of combinations with repetitions.

MSC:

90C31 Sensitivity, stability, parametric optimization
90C27 Combinatorial optimization
Full Text: DOI

References:

[1] Sergienko, I. V.; Kozeratskaya, L. N.; Lebedeva, T. T., Stability and Parametric Analysis of Discrete Optimization Problems (1995), Kiev: Naukova Dumka, Kiev · Zbl 0864.90096
[2] I. V. Sergienko, L. N. Kozeratskaya, and A. A. Kononova, “Stability and unboundedness of vector-optimization problems.” Kibern. Sist. Anal., No. 1, 3-10 (1997). · Zbl 0907.90236
[3] L. N. Kozeratskaya, T. T. Lebedeva, and I. V. Sergienko, “Stability of discrete-optimization problems,” Kibern. Sist. Anal., No. 3, 78-93 (1993). · Zbl 0829.90118
[4] L. N. Kozeratskaya, T. T. Lebedeva, and I. V. Sergienko, “Problems of stability and parametric and postoptimal analysis of discrete-optimization problems,” Kibernetika, No. 4, 71-80 (1983). · Zbl 0553.90069
[5] L. N. Kozeratskaya, T. T. Lebedeva, and I. V. Sergienko, “Discrete-optimization problems: Stability analysis,” Obozr. Prikl. Prom. Mat., No. 1, 12-30 (1995). · Zbl 0864.90096
[6] Kozeratskaya, L. N., Integer Optimization Problems: Stability Problems and Parametric Analysis (1997), Kiev: Author’s Abstract of Doctoral Dissertation, Kiev · Zbl 0916.90241
[7] Emelichev, V. A.; Berdysheva, R. A., Radii of pseudostability, quasistability, and stability of the vector trajectory problem of lexicographic optimization, Diskret. Mat., 10, 1, 20-27 (1998)
[8] V. A. Emelichev and M. K. Kravtsov, “Stability in vector optimization path problems” Kibern. Sist. Anal., No. 4, 137-143 (1995). · Zbl 0849.90103
[9] V. K. Leont’ev, “Stability in linear discrete problems,” Probl. Kibern., No. 35, 169-184 (1979). · Zbl 0439.93040
[10] Gordeev, E. N.; Leont’ev, V. K., Trajectory parametric problems, Zh. Vychisl. Mat. Mat. Fiz., 24, 1, 37-46 (1984) · Zbl 0566.90087
[11] Gordeev, E. N.; Leont’ev, V. K., The general approach to the analysis of the stability of discrete-optimization problems, Zh. Vychisl. Mat. Mat. Fiz., 36, 1, 66-72 (1996) · Zbl 1027.90526
[12] Stoyan, Yu. G.; Yemets, O. A., Theory and Methods of Euclidean Combinatorial Optimization (1993), Kiev: ISDO, Kiev
[13] Yemets, O. A., Theory and Methods of Combinatorial Optimization in Euclidean Sets in Geometric Designing (1997), Kiev: Author’s Abstract of Doctoral Dissertation, Kiev
[14] Yemets, O. A., Euclidean Combinatorial Sets and Optimization on Them. Advances in Mathematical Programming: A Textbook (1992), Kiev: UMK VO, Kiev
[15] Pichugina, O. S., Methods and Algorithms of Solution of Some Optimization Problems on Sets of Combinations and Permutations (1996), Khar’kov: HDTURE, Khar’kov
[16] M. Aigner, Combinatorial Theory [Russian translation], Mir, Moscow (1982). · Zbl 0415.05001
[17] Baranov, V. I.; Stechkin, B. S., Extremal Combinatorial Problems and Their Application (1989), Moscow: Nauka, Moscow · Zbl 0682.05002
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.