Linear-quadratic programming and its application to data correction of improper linear programming problems
The problem of maximizing a linear function with linear and quadratic constraints is considered. The solution of the problem is obtained in a constructive form using the Lagrange function and the optimality conditions. Many optimization problems can be reduced to the problem of this type. In this pa...
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| Veröffentlicht in: | Open computer science Jg. 10; H. 1; S. 48 - 55 |
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| Abstract | The problem of maximizing a linear function with linear and quadratic constraints is considered. The solution of the problem is obtained in a constructive form using the Lagrange function and the optimality conditions. Many optimization problems can be reduced to the problem of this type. In this paper, as an application, we consider an improper linear programming problem formalized in the form of maximization of the initial linear criterion with a restriction to the Euclidean norm of the correction vector of the right-hand side of the constraints or the Frobenius norm of the correction matrix of both sides of the constraints. |
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| AbstractList | The problem of maximizing a linear function with linear and quadratic constraints is considered. The solution of the problem is obtained in a constructive form using the Lagrange function and the optimality conditions. Many optimization problems can be reduced to the problem of this type. In this paper, as an application, we consider an improper linear programming problem formalized in the form of maximization of the initial linear criterion with a restriction to the Euclidean norm of the correction vector of the right-hand side of the constraints or the Frobenius norm of the correction matrix of both sides of the constraints. |
| Author | Zolotova, Tatiana Gorelik, Victor |
| Author_xml | – sequence: 1 givenname: Victor surname: Gorelik fullname: Gorelik, Victor email: vgor16@mail.ru organization: Dorodnicyn Computing Centre FRC CSC RAS, Moscow, Russia – sequence: 2 givenname: Tatiana surname: Zolotova fullname: Zolotova, Tatiana email: tgold11@mail.ru organization: Financial University under the Government of RF, Moscow, Russia |
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| References | Van Huffel (ref21) 1987 Gorelik (ref71) 2018; 8 Gorelik (ref61) 2017; 7 Golub (ref11) 1980; 17 Gorelik (ref41) 2001 Pardalos (ref81) 1991 Alizadeh (ref01) 1995 Martein (ref111) 1987; 12 Eremin (ref31) 1983 Erohin (ref51) 2007; 47 Floudas (ref101) 2009; 11 |
| References_xml | – volume: 47 start-page: 564 year: 2007 ident: ref51 article-title: correction of a dual pair of improper linear programming problems and publication-title: Matrix Computational Mathematics Mathematical Physics doi: 10.1134/S0965542507040033 – start-page: 11 year: 2001 ident: ref41 article-title: correction of a linear programming problem with inconsistent constraints and publication-title: Matrix Computational Mathematics Mathematical Physics – volume: 12 start-page: 75 year: 1987 ident: ref111 article-title: On solving a linear program with one quadratic constraint Decisions in publication-title: Economics Finance – volume: 8 start-page: 1 year: 2018 ident: ref71 article-title: Approximation of the improper linear programming problem with restriction on the norm of the correction matrix of the left - hand side of the constraints In of th International Conference on Optimization and Applications DEStech Transactions on Computer publication-title: Proceedings October Science Engineering – volume: 17 start-page: 883 year: 1980 ident: ref11 article-title: Loan An analysis of the total least squares problems publication-title: SIAM Numer Anal doi: 10.1137/0717073 – start-page: 1 year: 1991 ident: ref81 article-title: programming with one negative eigenvalue is hard of Optimization publication-title: Journal Global – start-page: 1 year: 1995 ident: ref01 article-title: Interior point methods in semidenite programming with applications to combinatorial optimization on Optimization publication-title: SIAM Journal – start-page: 149 year: 1987 ident: ref21 article-title: Algebraic relationships between classical regression and total least - squares estimation Linear Algebra and its Applications – year: 1983 ident: ref31 article-title: ev Improper linear and convex programming problems – volume: 7 start-page: 2017 year: 2017 ident: ref61 article-title: The problem of linear - quadratic programming In of th International Conference on Optimization and Applications publication-title: Proceedings October – volume: 11 year: 2009 ident: ref101 article-title: Editors Encyclopedia of Optimization |
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| SubjectTerms | data correction improper problem linear programming quadratic programming |
| Title | Linear-quadratic programming and its application to data correction of improper linear programming problems |
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