Fractional programming with absolute-value functions
This paper considers a fractional functionals programming problem of the type: maximize z= ∑ 1 nc j|x j|+α ∑ 1 nd j|x j|+β subject to Ax=b, x is unrestricted. In general, adjacent extreme point (simplex-type) methods [Naval Res. Logist. Quart. II (1964) 135] cannot be used to solve this class of pro...
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| Vydáno v: | European journal of operational research Ročník 141; číslo 1; s. 233 - 238 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier B.V
16.08.2002
Elsevier Elsevier Sequoia S.A |
| Edice: | European Journal of Operational Research |
| Témata: | |
| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | This paper considers a fractional functionals programming problem of the type:
maximize
z=
∑
1
nc
j|x
j|+α
∑
1
nd
j|x
j|+β
subject
to
Ax=b,
x is unrestricted. In general, adjacent extreme point (simplex-type) methods [Naval Res. Logist. Quart. II (1964) 135] cannot be used to solve this class of problems. However, this work presents the conditions under which simplex-type algorithms can be used to arrive at an optimal solution for a fractional programming problem with an absolute value objective function. |
|---|---|
| AbstractList | This paper considers a fractional functionals programming problem of the type:
maximize
z=
∑
1
nc
j|x
j|+α
∑
1
nd
j|x
j|+β
subject
to
Ax=b,
x is unrestricted. In general, adjacent extreme point (simplex-type) methods [Naval Res. Logist. Quart. II (1964) 135] cannot be used to solve this class of problems. However, this work presents the conditions under which simplex-type algorithms can be used to arrive at an optimal solution for a fractional programming problem with an absolute value objective function. This paper considers a fractional functionals programming problem of a specific type. In general, adjacent extreme point (simplex-type) methods [Naval Res. Logist. Quart. II (1964) 135] cannot be used to solve this class of problems. However, this work presents the conditions under which simplex-type algorithms can be used to arrive at an optimal solution for a fractional programming problem with an absolute value objective function. |
| Author | Chadha, S.S. |
| Author_xml | – sequence: 1 givenname: S.S. surname: Chadha fullname: Chadha, S.S. organization: Department of Mathematics, University of Wisconsin, Eau Claire, WI 54702, USA |
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| Cites_doi | 10.1002/nav.3800110204 10.1287/opre.19.1.120 10.1287/opre.13.6.1029 |
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| Keywords | Fractional programming Absolute value |
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| References | Swarup (BIB4) 1965; 13/6 Charnes, Cooper, Ferguson (BIB1) 1995; 1 Shanno, Weil (BIB3) 1971; 19/1 Martos (BIB2) 1964; II Shanno (10.1016/S0377-2217(01)00262-4_BIB3) 1971; 19/1 Charnes (10.1016/S0377-2217(01)00262-4_BIB1) 1995; 1 Martos (10.1016/S0377-2217(01)00262-4_BIB2) 1964; II Swarup (10.1016/S0377-2217(01)00262-4_BIB4) 1965; 13/6 |
| References_xml | – volume: 19/1 start-page: 120 year: 1971 end-page: 124 ident: BIB3 article-title: Linear programming with absolute-value functionals publication-title: Operations Research – volume: 13/6 start-page: 1029 year: 1965 end-page: 1036 ident: BIB4 article-title: Linear fractional functionals programming publication-title: Operations Research – volume: 1 start-page: 307 year: 1995 end-page: 323 ident: BIB1 article-title: Optimal estimation of executive compensation by linear programming publication-title: Management Sci. – volume: II start-page: 135 year: 1964 end-page: 155 ident: BIB2 article-title: Hyperbolic programming publication-title: Naval Research Logistics Quarterly – volume: II start-page: 135 year: 1964 ident: 10.1016/S0377-2217(01)00262-4_BIB2 article-title: Hyperbolic programming publication-title: Naval Research Logistics Quarterly doi: 10.1002/nav.3800110204 – volume: 19/1 start-page: 120 year: 1971 ident: 10.1016/S0377-2217(01)00262-4_BIB3 article-title: Linear programming with absolute-value functionals publication-title: Operations Research doi: 10.1287/opre.19.1.120 – volume: 13/6 start-page: 1029 year: 1965 ident: 10.1016/S0377-2217(01)00262-4_BIB4 article-title: Linear fractional functionals programming publication-title: Operations Research doi: 10.1287/opre.13.6.1029 – volume: 1 start-page: 307 year: 1995 ident: 10.1016/S0377-2217(01)00262-4_BIB1 article-title: Optimal estimation of executive compensation by linear programming publication-title: Management Sci. |
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| Snippet | This paper considers a fractional functionals programming problem of the type:
maximize
z=
∑
1
nc
j|x
j|+α
∑
1
nd
j|x
j|+β
subject
to
Ax=b,
x is unrestricted.... This paper considers a fractional functionals programming problem of a specific type. In general, adjacent extreme point (simplex-type) methods [Naval Res.... |
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| StartPage | 233 |
| SubjectTerms | Absolute value Fractional programming Mathematical models Problem solving Studies |
| Title | Fractional programming with absolute-value functions |
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