Lagrange multiplier characterizations of solution sets of constrained pseudolinear optimization problems. (English) Zbl 1124.90022
Summary: We study the minimization of a pseudolinear (i.e. pseudoconvex and pseudoconcave) function over a closed convex set subject to linear constraints. Various dual characterizations of the solution set of the minimization problem are given. As a consequence, several characterizations of the solution sets of linear fractional programs as well as linear fractional multi-objective constrained problems are given. Numerical examples are also given.
MSC:
| 90C26 | Nonconvex programming, global optimization |
| 90C29 | Multi-objective and goal programming |
| 90C30 | Nonlinear programming |
| 65K10 | Numerical optimization and variational techniques |
References:
| [1] | DOI: 10.1023/A:1004672604998 · Zbl 1039.49004 · doi:10.1023/A:1004672604998 |
| [2] | DOI: 10.1016/0167-6377(91)90087-6 · Zbl 0719.90055 · doi:10.1016/0167-6377(91)90087-6 |
| [3] | DOI: 10.1007/BF02612363 · Zbl 0534.90076 · doi:10.1007/BF02612363 |
| [4] | DOI: 10.1016/0022-247X(68)90201-1 · Zbl 0181.22806 · doi:10.1016/0022-247X(68)90201-1 |
| [5] | DOI: 10.1007/BF01581074 · Zbl 0771.90078 · doi:10.1007/BF01581074 |
| [6] | DOI: 10.1007/BF01581251 · Zbl 0789.90068 · doi:10.1007/BF01581251 |
| [7] | DOI: 10.1007/BF02192142 · Zbl 0840.90118 · doi:10.1007/BF02192142 |
| [8] | DOI: 10.1023/B:JOTA.0000043992.38554.c8 · Zbl 1114.90091 · doi:10.1023/B:JOTA.0000043992.38554.c8 |
| [9] | Jeyakumar V, European Journal of Operations Research |
| [10] | DOI: 10.1016/0377-2217(93)90069-Y · Zbl 0778.90064 · doi:10.1016/0377-2217(93)90069-Y |
| [11] | DOI: 10.1287/opre.15.5.882 · Zbl 0149.38006 · doi:10.1287/opre.15.5.882 |
| [12] | DOI: 10.1016/0167-6377(88)90047-8 · Zbl 0653.90055 · doi:10.1016/0167-6377(88)90047-8 |
| [13] | DOI: 10.1023/A:1023905907248 · Zbl 1043.90071 · doi:10.1023/A:1023905907248 |
| [14] | DOI: 10.1016/0377-2217(91)90267-Y · Zbl 0741.90067 · doi:10.1016/0377-2217(91)90267-Y |
| [15] | Rockafellar, RT. 1970. ”Convex Analysis”. Princeton, New Jersey: Princeton University Press. |
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