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Duality results on mathematical programs with vanishing constraints involving generalized invex functions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the here presented research, we investigate Wolfe and Mond-Weir duality models applied to a specific category of generalized convex functions known as p-invex functions. We establish various dualities between the primal MPVC and itsWolfe type dual, as well as between the primal MPVC (mathematical program with vanishing constraints) and its Mond-Weir type dual under p- invexity assumptions. To illustrate these theorems, we will include some examples.
Rocznik
Strony
351--379
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
  • Department of Mathematics, School of Advanced Engineering, UPES Dehradun 248007, India
Bibliografia
  • ACHTZIGER,W. and KANZOW, C. (2008) Mathematical programs with vanishing constraints: Optimality conditions and constraints qualifications. Mathematical Programming, 114 (1), 69–99.
  • ANTCZAK, T. (2001) On (p, r)-invexity-type nonlinear programming problems. Journal of Mathematical Analysis and Applications, 264 (2), 382–397.
  • ANTCZAK, T. (2010) G-saddle point criteria and G-Wolfe duality in differentiate mathematical programming. Journal of Information and Optimization Sciences, 31 (1), 63–85.
  • ANTCZAK, T. and SINGH, V. (2009) First-order optimality conditions and duality results for multi-objective optimization problems. Annals of Operations Research, 172 (1), 277–289.
  • ANTCZAK, T. and SINGH, V. (2013) Optimality and duality for minimax fractional programming with support functions under B-(p, r)- Type I assumptions. Mathematical and Computer Modelling, 57 (5-6), 1083 – 1100.
  • BOT, R. I. and GRAD, S.-M. (2010) Wolfe duality and Mond–Weir duality via perturbations. Nonlinear Analysis: Theory, Methods and Applications, 73 (2), 374–384.
  • CHINCHULUUN, A., YUAN, D. and PARDALOS, P. M. (2007) Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity. Annals of Operations Research, 154 (1), 133–147.
  • DUSSAULT, J.-P., MOUNIR H. and TANGI M. (2019) Mathematical programs with vanishing constraints: constraint qualifications, their applications, and a new regularization method. Optimization, 68 (2-3), 509–538.
  • HOHEISEL T. and KANZOWC. (2007) First and second-order optimality conditions for mathematical programs with vanishing constraints. Applications of Mathematics, 52, 495–514
  • HOHEISEL T. and KANZOW C. (2008) Stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications. Journal of Mathematical Analysis and Applications, 337, 292–310.
  • HOHEISEL T. and KANZOWC. (2009) On the Abadie and Guignard constraint qualification for mathematical progams with vanishing constraints. Optimization, 58, 431–448.
  • HU, Q. J., CHEN, Y., ZHU, Z. B. and ZHANG, B. S. (2014) Notes on some convergence properties for a smoothing regularization approach to mathematical programs with vanishing constraints. Abstract and Applied Analysis, 2014 (1), 1–7. https://doi.org/10.1155/2014/715015
  • HU, Q. J., WANG, J. G., CHEN, Y. and ZHU, Z. B. (2017) On an l1 exact penalty result for mathematical programs with vanishing constraints. Optimization Letters, 11 (3), 641–653.
  • HU, Q., WANG, J. and CHEN, Y. (2020) New dualities for mathematical programs with vanishing constraints. Annals of Operations Research, 287 (1), 233–255.
  • JABR, R. A. (2012) Solution to economic dispatching with disjoint feasible regions via semidefinite programming. IEEE Transactions on Power Systems, 27 (1), 572–573.
  • JOSHI, B. C. (2021a) Optimality and duality for nonsmooth semi-infinite mathematical program with equilibrium constraints involving generalized invexity of order a > 0. RAIRO - Operations Research, 55, 2221–2240.
  • JOSHI, B. C. (2021b) On generalized approximate convex functions and variational inequalities. RAIRO-Operations Research, 55, S2999–S3008.
  • JOSHI, B. C.,MISHRA, S. K. and KUMAR, P. (2020) On Semi-infiniteMathematical Programming Problems with Equilibrium Constraints Using Generalized Convexity. Journal of the Operations Research Society of China, 8 (4), 619–636.
  • KAZEMI, S. and KANZI, N. (2018) Constraint qualifications and stationary conditions for mathematical programming with non-differentiable vanishing constraints. Journal of Optimization Theory and Applications, 179 (3), 800–819.
  • MISHRA, S. K. and SHUKLA, K. (2010) Nonsmooth minimax programming problems with V -r-invex functions. Optimization, 59 (1), 95–103.
  • MISHRA, S. K., SINGH, V. and LAHA, V. (2016) On duality for mathematical programs with vanishing constraints. Annals of Operations Research, 243 (1), 249–272.
  • MICHAEL, N. J., KIRCHES, C. and SAGER, S. (2013) On perspective functions and vanishing constraints in mixedinteger nonlinear optimal control. In: M. Jünger and G. Reinelt, eds., Facets of Combinatorial Optimization, 387–417. Berlin: Springer.
  • MOND, B. and WEIR, T. (1981) Generalized concavity and duality. In: S. Schaible and W. T. Ziemba, eds., Generalized Concavity in Optimization and Economics, 263–279. New York: Academic Press.
  • SAGLAM, S. D. and MAHMUDOV, E. (2022) On Duality in Convex Optimization of Second-Order Differential Inclusions with Periodic Boundary Conditions. Hacettepe Journal of Mathematics and Statistics, 51 (6), 1588–1599.
  • TUNG, L. T. (2020) Karush–Kuhn–Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints. Annals of Operations Research, 311, 1307–1334.
  • TUNG, L. T. and TAM, D. H. (2021) Optimality Conditions and Duality for Multiobjective Semi-infinite Programming on Hadamard Manifolds. Bulletin of the Iranian Mathematical Society, 48, 2191–2219.
  • WOLFE, P. (1961) A duality theorem for nonlinear programming. Quarterly of Applied Mathematics, 19, 239–244.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-79f5d95a-9a20-43cb-8e8f-87d34afd4270
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