Free Access
RAIRO-Oper. Res.
Volume 55, Number 1, January-February 2021
Page(s) 247 - 260
Published online 15 March 2021
  • L. Armijo, Minimization of functions having lipschitz continuous first partial derivatives. Pac. J. Math. 16 (1966) 1–3. [CrossRef] [MathSciNet] [Google Scholar]
  • M.S. Bazaraa, H.D. Sherali and C.M. Shetty, Nonlinear Programming: Theory and Algorithms. John Wiley & Sons, New York (2013). [Google Scholar]
  • A. Beck and S. Sabach, A first order method for finding minimal norm-like solutions of convex optimization problems. Math. Program. 147 (2014) 25–46. [Google Scholar]
  • A. Callejo, F. Gholami, A. Enzenhöfer and J. Kövecses, Unique minimum norm solution to redundant reaction forces in multibody systems. Mech. Mach. Theory 116 (2017) 310–325. [Google Scholar]
  • Y.G. Evtushenko and A. Golikov, Theorems of alternative and optimization, in Optimization and Applications, edited by N. Olenev et al. In Vol. 12422 of Lecture Note in Computer Science. Springer, Cham (2020) 86–96. [Google Scholar]
  • Y.G. Evtushenko and A. Golikov, New perspective on the theorems of alternative. In: High Performance Algorithms and Software for Nonlinear Optimization, edited by G. Di Pillo and A. Murli. Vol. 82 of: Applied Optimization. Kluwer Academic Publishers Springer (2003) 227–241. [Google Scholar]
  • D. Gale, The Theory of Linear Economic Models. University of Chicago Press (1989). [Google Scholar]
  • M.S. Gockenbach and E. Gorgin, On the convergence of a heuristic parameter choice rule for Tikhonov regularization. SIAM J. Sci. Comput. 40 (2018) A2694–A2719. [Google Scholar]
  • A.I. Golikov and Y.G. Evtushenko, Theorems of the alternative and their applications in numerical methods. Comput. Math. Math. Phys. 43 (2003) 338–358. [Google Scholar]
  • E.R. Hansen and G.W. Walster, Global Optimization Using Interval Analysis, 2nd edition. Marcel Dekker, New York (2004). [Google Scholar]
  • J.-B. Hiriart-Urruty, J.-J. Strodiot and V.H. Nguyen, Generalized Hessian matrix and second-order optimality conditions for problems with C1,1 data. Appl. Math. Optim. 11 (1984) 43–56. [Google Scholar]
  • L. Jaulin, M. Kieffer, O. Didrit and É. Walter, Applied Interval Analysis. Springer, London (2001). [Google Scholar]
  • C. Kanzow, H. Qi and L. Qi, On the minimum norm solution of linear programs. J. Optim. Theory App. 116 (2003) 333–345. [Google Scholar]
  • S. Ketabchi and E. Ansari-Piri, On the solution set of convex problems and its numerical application. J. Comput. Appl. Math. 206 (2007) 288–292. [Google Scholar]
  • S. Ketabchi and H. Moosaei, Minimum norm solution to the absolute value equation in the convex case. J. Optim. Theory App. 154 (2012) 1080–1087. [Google Scholar]
  • S. Kindermann and K. Raik, Convergence of heuristic parameter choice rules for convex Tikhonov regularization. SIAM J. Numer. Anal. 58 (2020) 1773–1800. [Google Scholar]
  • O.L. Mangasarian, A simple characterization of solution sets of convex programs. Oper. Res. Lett. 7 (1988) 21–26. [Google Scholar]
  • O.L. Mangasarian, A Finite newton method for classification. Optim. Methods Softw. 17 (2002) 913–929. [Google Scholar]
  • P.M. Pardalos, S. Ketabchi and H. Moosaei, Minimum norm solution to the positive semidefinite linear complementarity problem. Optimization 63 (2014) 359–369. [Google Scholar]
  • O. Prokopyev, On equivalent reformulations for absolute value equations. Comput. Optim. App. 44 (2009) 363–372. [Google Scholar]
  • J.B. Rosen, Minimum norm solution to the linear complementarity problem. In: Functional Analysis, Optimization and Mathematical Economics, edited by L.J. Leifman et al. Oxford University Press, Oxford (1990) 208–216. [Google Scholar]
  • A.N. Tikhonov and V.I. Arsenin, Solutions of Ill-Posed Problems. Winston, Washington, DC (1977). [Google Scholar]
  • X.-H. Vu, D. Sam-Haroud and M.-C. Silaghi, Numerical constraint satisfaction problems with non-isolated solutions. In: Global Optimization and Constraint Satisfaction, edited by C. Bliek, C. Jermann and A. Neumaier. Springer, Berlin-Heidelberg (2003) 194–210. [Google Scholar]
  • J. Wang and Y. Xia, A dual neural network solving quadratic programming problems. In: Vol. 1 of IJCNN’99. International Joint Conference on Neural Networks. Proceedings (Cat. No. 99CH36339). IEEE (1999) 588–593. [Google Scholar]
  • Y. Yao, R. Chen and H.-K. Xu, Schemes for finding minimum-norm solutions of variational inequalities. Nonlinear Anal.: Theory Methods App. 72 (2010) 3447–3456. [Google Scholar]

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