Asymptotic behavior of semi-quasivariational optimistic bilevel problems in Banach spaces
The great interest into hierarchical optimization problems and the increasing use of game theory in many economic or engineering applications led to investigate scalar bilevel problems in which the upper level is an optimization problem and the lower level is a parametrized quasi-variational inequal...
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| Published in: | Journal of mathematical analysis and applications Vol. 424; no. 1; pp. 1 - 20 |
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| Abstract | The great interest into hierarchical optimization problems and the increasing use of game theory in many economic or engineering applications led to investigate scalar bilevel problems in which the upper level is an optimization problem and the lower level is a parametrized quasi-variational inequality. In this paper, we analyze the convergence of the sequences of infima and minima for the upper level when the data of the problem are perturbed. First, we show that general results on the convergence of the infima and minima may not be possible. Thus, we introduce suitable concepts of regularized semi-quasivariational optimistic bilevel problems and we study, in Banach spaces, the convergence properties of the infima and minima to these regularized problems in the presence or not of perturbations. |
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| AbstractList | The great interest into hierarchical optimization problems and the increasing use of game theory in many economic or engineering applications led to investigate scalar bilevel problems in which the upper level is an optimization problem and the lower level is a parametrized quasi-variational inequality. In this paper, we analyze the convergence of the sequences of infima and minima for the upper level when the data of the problem are perturbed. First, we show that general results on the convergence of the infima and minima may not be possible. Thus, we introduce suitable concepts of regularized semi-quasivariational optimistic bilevel problems and we study, in Banach spaces, the convergence properties of the infima and minima to these regularized problems in the presence or not of perturbations. |
| Author | Lignola, M. Beatrice Morgan, Jacqueline |
| Author_xml | – sequence: 1 givenname: M. Beatrice surname: Lignola fullname: Lignola, M. Beatrice email: lignola@unina.it organization: Department of Mathematics and Applications R. Caccioppoli, University of Naples Federico II, Via Claudio, 80125 Naples, Italy – sequence: 2 givenname: Jacqueline surname: Morgan fullname: Morgan, Jacqueline email: morgan@unina.it organization: Department of Economics and Statistics & CSEF, University of Naples Federico II, Via Cinthia, 80126 Naples, Italy |
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| References | Lignola, Morgan (br0140) 1994; 8-B Lignola, Morgan (br0210) 2012; 53 Fukushima, Pang (br0110) 2005; 2 Aubin (br0020) 1979 Rockafellar, Wets (br0270) 1998 Drouet, Haurie, Moresino, Vial, Vielle, Viguier (br0100) 2008; 5 Loridan, Morgan (br0240) 1996; 8 Aubin, Frankowska (br0030) 1990 Bonnel, Morgan (br0050) 2006; 131 Lignola, Morgan (br0150) 1994; 49 Baiocchi, Capelo (br0040) 1984 Lignola, Morgan (br0190) 2001 Dal Maso (br0080) 1993 Lignola, Morgan (br0160) 1997; 93 Colson, Marcotte, Savard (br0070) 2007; 153 Lignola, Morgan (br0200) 2012; 19 Dempe (br0090) 2002 Harker, Pang (br0120) 1990; 48 Lignola, Morgan (br0180) 1999; 101 Lignola (br0130) 2006; 128 Lignola, Morgan (br0220) 2014; 10 Attouch (br0010) 1984 Morgan, Prieur (br0260) 2013; 18 Loridan, Morgan (br0230) 1989; 20 Luo, Pang, Ralph (br0250) 1996 Breton, Alj, Haurie (br0060) 1988; 59 Lignola, Morgan (br0170) 1997; 10 Fukushima (10.1016/j.jmaa.2014.10.059_br0110) 2005; 2 Lignola (10.1016/j.jmaa.2014.10.059_br0190) 2001 Colson (10.1016/j.jmaa.2014.10.059_br0070) 2007; 153 Lignola (10.1016/j.jmaa.2014.10.059_br0200) 2012; 19 Rockafellar (10.1016/j.jmaa.2014.10.059_br0270) 1998 Morgan (10.1016/j.jmaa.2014.10.059_br0260) 2013; 18 Lignola (10.1016/j.jmaa.2014.10.059_br0180) 1999; 101 Baiocchi (10.1016/j.jmaa.2014.10.059_br0040) 1984 Lignola (10.1016/j.jmaa.2014.10.059_br0160) 1997; 93 Dal Maso (10.1016/j.jmaa.2014.10.059_br0080) 1993 Lignola (10.1016/j.jmaa.2014.10.059_br0150) 1994; 49 Loridan (10.1016/j.jmaa.2014.10.059_br0230) 1989; 20 Aubin (10.1016/j.jmaa.2014.10.059_br0030) 1990 Dempe (10.1016/j.jmaa.2014.10.059_br0090) 2002 Lignola (10.1016/j.jmaa.2014.10.059_br0210) 2012; 53 Lignola (10.1016/j.jmaa.2014.10.059_br0130) 2006; 128 Aubin (10.1016/j.jmaa.2014.10.059_br0020) 1979 Lignola (10.1016/j.jmaa.2014.10.059_br0220) 2014; 10 Attouch (10.1016/j.jmaa.2014.10.059_br0010) 1984 Harker (10.1016/j.jmaa.2014.10.059_br0120) 1990; 48 Lignola (10.1016/j.jmaa.2014.10.059_br0170) 1997; 10 Luo (10.1016/j.jmaa.2014.10.059_br0250) 1996 Drouet (10.1016/j.jmaa.2014.10.059_br0100) 2008; 5 Loridan (10.1016/j.jmaa.2014.10.059_br0240) 1996; 8 Bonnel (10.1016/j.jmaa.2014.10.059_br0050) 2006; 131 Lignola (10.1016/j.jmaa.2014.10.059_br0140) 1994; 8-B Breton (10.1016/j.jmaa.2014.10.059_br0060) 1988; 59 |
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| Title | Asymptotic behavior of semi-quasivariational optimistic bilevel problems in Banach spaces |
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