An LP-based algorithm for the correction of inconsistent linear equation and inequality systems

References

• Baumgart , R. and Beer , K. 1990 . Ein Decompositionzugang in inkonsistenten linearen Optimierungsaufgaben . Wiss. Z. d. TU Karl-Marx-Stadt , 32 ( 1 ) : 56 – 64 .
   Google Scholar
• Bulavskij , V.A. 1985 . “ Generalized solutions and regularization of inequality systems ” . In Vichislitelnye metody linejnoj algebry 161 – 174 . Nauka Novosibirsk, Russian
   Google Scholar
• Burke , J.N. 1989 . A sequential quadratic programming method for potentially infeasible mathematical programs . J. Math. Anal. Appl , 139 ( 2 ) : 319 – 351 .
   Web of Science ®Google Scholar
• Davidov , E.G. 1989 . On the inconsistent linear equation systems . Vestnik MGU, Ser , 15 ( 2 ) : 76 – 79 . Russian
   Google Scholar
• Elving , T. 1980 . Block-Iterative methods for consistent and inconsistent linear equations . Numer. Math , 35 ( 1 ) : 1 – 12 .
   Web of Science ®Google Scholar
• Eremin , I.I. 1988 . Contradictory Models of Optimal Planning Nauka Moscow, (Russian)
   Google Scholar
• Eremin , I.I. , Mazurov , V.D. and Astaf’ev , N.N. 1983 . Improper Problems of Linear and Convex Programming. Nauka, Moscow Nauka Moscow, (Russian)
   Google Scholar
• Eremin , I.I. and Vatolin , A.A. 1989 . Improper mathematical programming problems . Problems Contr. Inform. Theory , 18 ( 6 ) : 359 – 380 .
   Google Scholar
• Lasserre , J.B. 1986 . Consistency of a linear system of inequalities . J. Optim. Theory Appl , 49 ( 1 ) : 177 – 179 .
   Web of Science ®Google Scholar
• Mangasarian , O.L. 1984 . Normal solutions of linear programs . Math. Progr. Study , 22 ( 1 ) : 206 – 212 .
   Google Scholar
• Martinez-Legaz , J.E. 1984 . Lexicographical order, inequality systems and optimization . Lect. Notes Contr. Inf. Sci , 59 ( 1 ) : 203 – 212 .
   Google Scholar
• Marusciac , I. 1986 . Simplex-like method for the Pareto minimum solutions of an inconsistent system . Studia Univ. Babes-Bolyai Math , 31 ( 4 ) : 22 – 30 .
   Google Scholar
• Marusciac , I. 1987 . “ Duality theorems for constraint Pareto minimum solutions of a linear system ” . In Prepr , Babes-Bolyai Univ .
   Google Scholar
• Schnabel , R.B. 1982 . Determining feasibility of a set of nonlinear inequality constraints . Math. Progr. Study , 16 : 137 – 148 .
   Google Scholar
• Skarin , V.D. 1986 . On an approach to the analysis of improper problems of linear programming . Zh. Vichisl. Matem. i Matem. Phis , 26 ( 3 ) : 439 – 448 . Russian
   Google Scholar
• Solukvadse , M.E. and Topchishvili , A.L. 1989 . Insoluble multicriteria linear programming problems . J. Opt. Theory Appl , 61 ( 3 ) : 487 – 491 .
   Web of Science ®Google Scholar
• Vatolin A. A. On the approximation of inconsistent linear equation and inequality systems Metody Approximatsii Nesobstvennih Zadach Matematicheskogo Programmirovanija 1984 UNTs AN SSSR, Sverdlovsk Russian 39 54
   Google Scholar
• Vatolin , A.A. 1984 . Approximation of improper linear programs using Eucleadian norm criterion . Zh. Vichisl. Matem. i Matem. Phys , 24 ( 12 ) : 1907 – 1908 . Russian
   Google Scholar
• Vatolin , A.A. 1986 . Parametric approximation of inconsistent systems of linear equations and inequalities . Seminarber , 81 : 145 – 154 .
   Google Scholar
• Vatolin , A.A. 1987 . Correction of inconsistent linear inequality system with regard to restrictions on parameter variation , 90 : 132 – 135 .
   Google Scholar
• Vatolin A. A. Solvability sets and correction of saddle functions and inequality systems Ural Branch Acad. Sci. USSR Sverdlovsk 1989 Prepr. (Russian)
   Google Scholar
• Vereskov , A.I. and Tret’jakov , N.W. 1988 . On the application of augmented Lagrangeans to the correction of inconsistent convex programs . Izvestija AN SSSR, Tech. Kib , 1 : 3 – 12 . Russian
   Google Scholar