Some results related to constrained non-differentiable (non-smooth) pseudolinear minimization problems
Journal of Contemporary Issues in Business and Government,
2021, Volume 27, Issue 3, Pages 1480-1486
10.47750/cibg.2021.27.03.199
Abstract
This paper deals with the minimization of a class of non-differentiable (non-smooth) pseudolinear functions over a closed and convex set subject to linear inequality constraints. The properties of locally Lipschitz pseudolinear functions are used to establish several Lagrange multiplier characterizations of the solution set of the minimization problem. We derive certain conditions, under which an efficient solution becomes a properly efficient solution of a constrained non-differentiable minimization problem.
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- O.L. Mangasarian: A simple characterization of solution sets of convex programs. Oper. Res. Lett. 7, 21-26, (1988).
- V. Jeyakumar, H. Wolkowicz: Generalizations of Slater’s constraint qualification for infinite convex programs. Math. Program. 57, 551-571, (1992).
- V. Jeyakumar: Infinite dimensional convex programming with applications to constrained approximation. J. Optim. Theory Appl. 75(3), 469-486 (1992)
- J.V. Burke, M.C. Ferris: Characterization of solution sets of convex programs. Oper. Res. Lett. 10, 57-60, (1991).
- V. Jeyakumar, X.Q. Yang: Convex composite multiobjective nonsmooth programming. Math. Program. 59, 325-343, (1993).
- V. Jeyakumar, X.Q. Yang: On characterizing the solution sets of pseudolinear programs. J. Optim. Theory Appl. 87, 747-755, (1995).
- V. Jeyakumar, G.M. Lee, N. Dinh: Lagrange multiplier conditions characterizing optimal solution sets of cone-constrained convex programs. J. Optim. Theory Appl. 123, 83-103, (2004).
- V. Jeyakumar, G.M. Lee, N. Dinh: Characterization of solution sets of convex vector optimization programs. Eur. J. Oper. Res. 174, 1380-1395, (2006).
- O.L. Mangasarian: Nonlinear Programming. McGraw-Hill, New York, (1969).
- K.L. Chew, E.U. Choo: Pseudolinearity and efficiency. Math. Program. 28, 226-239, (1984).
- S. Komlosi: First and second-order characterization of pseudolinear functions. Eur. J. Oper. Res. 15, 882-891, (1993).
- Q.H. Lu, D.L. Zhu: Some characterization of locally Lipschtiz pseudolinear functions. Math. Appl. 18, 272-278, (2005).
- N. Dinh, V. Jeyakumar, G.M. Lee: Lagrange multiplier characterizations of solution sets of constrained pseudolinear optimization problems. Optimization 55(3), 241-250, (2006).
- S.K. Mishra, B.B. Upadhyay: Duality in non-smooth multi-objective programming involving 𝜂- pseudolinear functions. Indian J. Indust. Appl. Math. 3(1s), 152-161, (2012).
- F.H. Clarke: Optimization and Non-smooth Analysis. John Wiley and Sons, New York, (1983).
- D. Aussel: Subdifferential properties of quasiconvex and pseudoconvex functions: unified approach. J. Optim. Theory Appl. 97, 29-45, (1998).
- K.Q. Zhao, L.P. Tang: On characterizing solution set of non-differentiable 𝜂-pseudolinear extremum problem. Optimization 61(3), 239-249, (2012).
- R.T. Rockafellar: Convex Analysis. Princeton University Press, Princeton, (1970).
- A.M. Geoffrion: Proper efficiency and theory of vector maximization. J. Math. Anal. Appl. 22, 618-630, (1968).
- Patidar Manmohan, Bhardwaj Ramakant, Choudhary Sanjay. “The Study of Linear Programming Approach for Optimal Scheduling of Work in A Corporation with Different Models.” Materials Today: Proceedings No 29, 661–667 (2020)
- A.K.Jain, R.K.Bhardwaj, H.Saxena, A.Choubey, Application of Linear Programming for Profit Maximization of the Bank and the Investor, International Journal of Engineering and Advanced Technology No 8,4166-4168(2019)
- A.K.Jain, H.Saxena, S.Chouhan, R.K.Bhardwaj, Application of Linear Programming in Nurse Scheduling, TEST(Engineering and Management) No 83, 867-870 (2020)
- A.K.Jain, H.Saxena, R.K.Bhardwaj, G.V.V.Jagannadha Rao, Ch.Siddharth Nanda, Application of Linear Programming for Profit Maximization of a Pharma Company, Journal of Critical Reviews .No 7 , 1118-1123 (2020)
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