Some remarks on duality and optimality of a class of constrained convex quadratic minimization problems

Authors

  • Sudipta Roy Lady Brabourne College, Department of Mathematics, Kolkata, India
  • Sandip Chatterjee Heritage Institute of Technology, Kolkata, India
  • R.N. Mukherjee University of Burdwan, Department of Mathematics, India

DOI:

https://doi.org/10.2298/YJOR170119012R

Keywords:

quadratic forms, semidefinite matrices, lagrangian duality

Abstract

In this paper the duality and optimality of a class of constrained convex quadratic optimization problems have been studied. Furthermore, the global optimality condition of a class of interval quadratic minimization problems has also been discussed.

References

Andersen, E.D., Roos, C., Terlaky, T., "On Implementing a Primal-Dual Interior-Point Method for Conic Quadratic Optimization", Mathematical Programming, Series B, 95 (2003) 249-277.

Beck, A., Terboulle, M., "Global Optimality Conditions for Quadratic Optimization Problems with Binary Constraints", SIAM Journal on Optimization, 11 (1) (2000) 179-188.

Beck, A., Eldar, C.Y., "Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints", SIAM Journal on Optimization, 17 (3) (2006) 844-860.

Ben-Israel, A., Greville, T.N.E., Generalized Inverses: Theory and Applications, Canadian Mathematical Society, USA, 1973.

Blekherman, G., Parrilo, P.A., Thomas, R.R., Semidefinite Optimization and Convex Algebraic Geometry, SIAM and Mathematical Optimization Society, Philadelphia, USA, 2013.

Bomze, I.M., "Branch-and-Bound Approaches to Standard Quadratic Optimization Problems", Journal of Global Optimization, 22 (2002) 17-37.

Bomze, I.M., Palagi, L., "Quartic Formulation of Standard Quadratic Optimization Problems", Journal of Global Optimization, 32 (2005) 181-205.

Bomze, I.M., Locatelli, M., "Separable Standard Quadratic Optimization Problems", Optimization Letters, doi: 10.1007/s11590-011-0309-z (2011).

Bomze, I.M., Grippo, L., Palagi, L., "Unconstrained Formulation of Standard Quadratic Optimization Problems", TOP, doi: 10.1007/s11750-010-0166-4 (2010).

Boyd, S., Vandenberghe, L., Convex Optimization, Cambridge University Press, UK, 2004.

Chatterjee, S., Mukherjee, R.N., "On Invex Functions in Hilbert Space", Journal of Information and Optimization Sciences, 37 (1) (2016) 1-11.

Horst, R., Pardalos, P.M., Handbook of Global Optimization, Springer, New York, (1995).

Man-Cho So, A., Zhang, J., Ye, Y., "On Approximating Complex Quadratic Optimization Problems via Semidefinite Programming Relaxations", Mathematical Programming, Series B, doi: 10.1007/s10107-006-0064-6 (2006).

Nesterov, E.Y., Todd, M.J., "Primal-Dual Interior-Point Methods for Self-Scaled Cones", SIAM Journal on Optimization, 8 (2) (1998) 324-364.

Rockafellar, R.T., Convex Analysis, Princeton University Press, USA, 1970.

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Published

2017-05-01

Issue

Vol. 27 No. 2 (2017)

Section

Research Articles

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