Calmness of Linear Constraint Systems under Structured Perturbations with an Application to the Path-Following Scheme
We are concerned with finite linear constraint systems in a parametric framework where the right-hand side is an affine function of the perturbation parameter. Such structured perturbations provide a unified framework for different parametric models in the literature, as block, directional and/or pa...
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| Vydáno v: | Set-valued and variational analysis Ročník 29; číslo 4; s. 839 - 860 |
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| Jazyk: | angličtina |
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Springer Netherlands
01.12.2021
Springer Nature B.V |
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| ISSN: | 1877-0533, 1877-0541 |
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| Abstract | We are concerned with finite linear constraint systems in a parametric framework where the right-hand side is an affine function of the perturbation parameter. Such structured perturbations provide a unified framework for different parametric models in the literature, as block, directional and/or partial perturbations of both inequalities and equalities. We extend some recent results about calmness of the feasible set mapping and provide an application to the convergence of a certain path-following algorithmic scheme. We underline the fact that our formula for the calmness modulus depends only on the nominal data, which makes it computable in practice. |
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| AbstractList | We are concerned with finite linear constraint systems in a parametric framework where the right-hand side is an affine function of the perturbation parameter. Such structured perturbations provide a unified framework for different parametric models in the literature, as block, directional and/or partial perturbations of both inequalities and equalities. We extend some recent results about calmness of the feasible set mapping and provide an application to the convergence of a certain path-following algorithmic scheme. We underline the fact that our formula for the calmness modulus depends only on the nominal data, which makes it computable in practice. |
| Author | Argáez, C. Cánovas, M.J. Parra, J. |
| Author_xml | – sequence: 1 givenname: C. surname: Argáez fullname: Argáez, C. organization: Faculty of Physical Sciences, University of Iceland – sequence: 2 givenname: M.J. surname: Cánovas fullname: Cánovas, M.J. organization: Center of Operations Research, Miguel Hernández University of Elche – sequence: 3 givenname: J. orcidid: 0000-0001-8864-975X surname: Parra fullname: Parra, J. email: parra@umh.es organization: Center of Operations Research, Miguel Hernández University of Elche |
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| Keywords | 90C31 Feasible set mapping 90C51 49J53 Linear programming 90C05 Calmness Linear systems of equalities and inequalities Primal-dual path-following algorithm |
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| References | Cánovas, López, Parra, Toledo (CR11) 2014; 22 Cánovas, Parra, Rückmann, Toledo (CR12) 2017; 25 Zhang, Tapia, Dennis (CR36) 1992; 2 Cánovas, Gómez-Senent, Parra (CR5) 2012; 19 Al-Jeiroudi, Gondzio, Hall (CR1) 2008; 23 Klatte, Kummer (CR22) 2009; 117 Klatte, Kummer (CR23) 2018; 168 Gondzio (CR16) 2012; 218 Potra (CR31) 2001; 91 Kruger, Ngai, Théra (CR24) 2010; 20 CR35 Cánovas, Klatte, López, Parra (CR8) 2007; 18 Mangasarian, Fromovitz (CR26) 1967; 17 Renegar (CR32) 1988; 40 Cánovas, Henrion, López, Parra (CR7) 2016; 169 Goberna, López (CR15) 1998 Ioffe (CR19) 2017 Li, Meng, Yang (CR25) 2018; 171 Karmarkar (CR20) 1984; 4 Cánovas, Hall, López, Parra (CR6) 2019; 68 Rockafellar, Wets (CR34) 1998 Facchinei, Fischer, Herrich (CR14) 2014; 146 Klatte, Kummer (CR21) 2002 Hoffman (CR18) 1952; 49 Rockafellar (CR33) 1970 Monteiro, Adler (CR28) 1989; 44 CR4 Dontchev, Rockafellar (CR13) 2009 Bai, Ye, Zhang (CR2) 2019; 29 CR27 Potra, Wright (CR30) 2000; 124 Bazaraa, Sherali, Shetty (CR3) 1993 Cánovas, López, Mordukhovich, Parra (CR9) 2012; 20 Cánovas, López, Mordukhovich, Parra (CR10) 2020; 48 Hu (CR17) 2005; 30 Mordukhovich (CR29) 2006 MJ Cánovas (597_CR5) 2012; 19 D Klatte (597_CR22) 2009; 117 MJ Cánovas (597_CR10) 2020; 48 F Facchinei (597_CR14) 2014; 146 MJ Cánovas (597_CR11) 2014; 22 G Al-Jeiroudi (597_CR1) 2008; 23 MA Goberna (597_CR15) 1998 H Hu (597_CR17) 2005; 30 J Renegar (597_CR32) 1988; 40 K Bai (597_CR2) 2019; 29 MJ Cánovas (597_CR12) 2017; 25 FA Potra (597_CR31) 2001; 91 J Gondzio (597_CR16) 2012; 218 RT Rockafellar (597_CR34) 1998 597_CR4 D Klatte (597_CR23) 2018; 168 BS Mordukhovich (597_CR29) 2006 MJ Cánovas (597_CR6) 2019; 68 MS Bazaraa (597_CR3) 1993 N Karmarkar (597_CR20) 1984; 4 D Klatte (597_CR21) 2002 RT Rockafellar (597_CR33) 1970 FA Potra (597_CR30) 2000; 124 597_CR35 MJ Cánovas (597_CR7) 2016; 169 AJ Hoffman (597_CR18) 1952; 49 A Kruger (597_CR24) 2010; 20 MH Li (597_CR25) 2018; 171 Y Zhang (597_CR36) 1992; 2 AL Dontchev (597_CR13) 2009 OL Mangasarian (597_CR26) 1967; 17 RDC Monteiro (597_CR28) 1989; 44 MJ Cánovas (597_CR9) 2012; 20 597_CR27 AD Ioffe (597_CR19) 2017 MJ Cánovas (597_CR8) 2007; 18 |
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| Title | Calmness of Linear Constraint Systems under Structured Perturbations with an Application to the Path-Following Scheme |
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