{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,22]],"date-time":"2024-03-22T12:27:30Z","timestamp":1711110450067},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T00:00:00Z","timestamp":1532563200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"The third-named author was partially supported by a grant from IPM"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2018,12]]},"DOI":"10.1007\/s10957-018-1336-z","type":"journal-article","created":{"date-parts":[[2018,7,26]],"date-time":"2018-07-26T16:05:31Z","timestamp":1532621131000},"page":"778-799","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Constraint Qualifications and Sensitivity Analysis for General Optimization Problems via Pseudo-Jacobians"],"prefix":"10.1007","volume":"179","author":[{"given":"M. Alavi","family":"Hejazi","sequence":"first","affiliation":[]},{"given":"N.","family":"Movahedian","sequence":"additional","affiliation":[]},{"given":"S.","family":"Nobakhtian","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,7,26]]},"reference":[{"key":"1336_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2825-5","volume-title":"Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory","author":"JV Outrata","year":"1998","unstructured":"Outrata, J.V., Kocvara, M., Zowe, J.: Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory. Applications and Numerical Results. Kluwer Academic Publishers, Boston (1998)"},{"key":"1336_CR2","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1007\/BFb0120989","volume":"19","author":"SM Robinson","year":"1982","unstructured":"Robinson, S.M.: Generalized equations and their solution, part \n                    \n                      \n                    \n                    $$\\rm {II}$$\n                    \n                      \n                        II\n                      \n                    \n                  : Applications to nonlinear programming. Math. Program. Stud. 19, 200\u2013221 (1982)","journal-title":"Math. Program. Stud."},{"key":"1336_CR3","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0074500","volume-title":"Methods of Descent for Nondifferentiable Optimization","author":"KC Kiwiel","year":"1985","unstructured":"Kiwiel, K.C.: Methods of Descent for Nondifferentiable Optimization. Lecture Notes in Mathematics, vol. 1133. Springer, New York (1985)"},{"key":"1336_CR4","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1007\/s10957-012-0167-6","volume":"157","author":"AM Bagirov","year":"2013","unstructured":"Bagirov, A.M., Jin, L., Karmitsa, N., Al Nuaimat, A., Sultanova, N.: Subgradient method for nonconvex nonsmooth optimization. J. Optim. Theory and Appl. 157, 416\u2013435 (2013)","journal-title":"J. Optim. Theory and Appl."},{"key":"1336_CR5","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1137\/030601296","volume":"15","author":"JV Burke","year":"2005","unstructured":"Burke, J.V., Lewis, A.C., Overton, M.L.: A robust gradient sampling algorithm for nonsmooth, nonconvex optimization. SIAM J. Optim. 15, 571\u2013779 (2005)","journal-title":"SIAM J. Optim."},{"key":"1336_CR6","doi-asserted-by":"publisher","first-page":"1815","DOI":"10.1137\/S0363012996311745","volume":"36","author":"V Jeyakumar","year":"1998","unstructured":"Jeyakumar, V., Luc, D.T.: Approximate Jacobian matrices for nonsmooth continuous maps and \n                    \n                      \n                    \n                    $$c^1$$\n                    \n                      \n                        \n                          c\n                          1\n                        \n                      \n                    \n                  -optimization. SIAM J. Control Optim. 36, 1815\u20131832 (1998)","journal-title":"SIAM J. Control Optim."},{"key":"1336_CR7","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1023\/A:1021790120780","volume":"101","author":"V Jeyakumar","year":"1999","unstructured":"Jeyakumar, V., Luc, D.T.: Nonsmooth calculus, minimality, and monotonicity of convexificators. J. Optim. Theory Appl. 101, 599\u2013621 (1999)","journal-title":"J. Optim. Theory Appl."},{"key":"1336_CR8","volume-title":"Nonsmooth Vector Functions and Continuous Optimization","author":"V Jeyakumar","year":"2007","unstructured":"Jeyakumar, V., Luc, D.T.: Nonsmooth Vector Functions and Continuous Optimization. Springer, New York (2007)"},{"key":"1336_CR9","doi-asserted-by":"publisher","first-page":"1106","DOI":"10.1137\/S1052623402419236","volume":"14","author":"V Jeyakumar","year":"2004","unstructured":"Jeyakumar, V., Yen, N.D.: Solution stability of nonsmooth continuous systems with applications to cone-constrained optimization. SIAM J. Optim. 14, 1106\u20131127 (2004)","journal-title":"SIAM J. Optim."},{"key":"1336_CR10","doi-asserted-by":"publisher","first-page":"2566","DOI":"10.1016\/j.na.2011.11.003","volume":"75","author":"J Zhang","year":"2012","unstructured":"Zhang, J., Zhang, L., Wang, W.: On constraint qualifications in terms of approximate \n                    \n                      \n                    \n                    $$\\rm {J}$$\n                    \n                      \n                        J\n                      \n                    \n                  acobians for nonsmooth continuous optimization problems. Nonlinear Anal. 75, 2566\u20132680 (2012)","journal-title":"Nonlinear Anal."},{"key":"1336_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation Analysis of Optimization Problems","author":"JF Bonnans","year":"2000","unstructured":"Bonnans, J.F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New York (2000)"},{"key":"1336_CR12","volume-title":"Nonsmooth Analysis and Control Theory","author":"FH Clarke","year":"1998","unstructured":"Clarke, F.H., Ledyaev, Y.S., Wolenski, R.S.P.: Nonsmooth Analysis and Control Theory. Springer, NewYork (1998)"},{"key":"1336_CR13","doi-asserted-by":"publisher","first-page":"1309","DOI":"10.1137\/110845197","volume":"22","author":"S Demp","year":"2012","unstructured":"Demp, S., Mordukhovich, B.S., Zemkoho, A.B.: Sensitivity analysis for two-level value functions with applications to bilevel progrmming. SIAM J. Optim. 22, 1309\u20131343 (2012)","journal-title":"SIAM J. Optim."},{"key":"1336_CR14","volume-title":"Introduction to Sensitivity and Stability Analysis in Nonlinear Programming","author":"AV Fiacco","year":"1983","unstructured":"Fiacco, A.V.: Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Academic Press, New York (1983)"},{"key":"1336_CR15","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/BFb0120984","volume":"19","author":"J Gauvin","year":"1982","unstructured":"Gauvin, J., Dubeau, F.: Differential properties of the marginal function in mathematical programming. Math. Program. Stud. 19, 101\u2013119 (1982)","journal-title":"Math. Program. Stud."},{"key":"1336_CR16","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/s10107-007-0120-x","volume":"116","author":"BS Mordukhovich","year":"2009","unstructured":"Mordukhovich, B.S., Nam, N.M., Yen, N.D.: Subgradients of marginal functions in parametric mathematical programming. Math. Program. 116, 369\u2013396 (2009)","journal-title":"Math. Program."},{"key":"1336_CR17","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/BF02591866","volume":"26","author":"RT Rockafellar","year":"1983","unstructured":"Rockafellar, R.T.: Marginal values and second-order necessary conditions for optimality. Math. Program. 26, 245\u2013286 (1983)","journal-title":"Math. Program."},{"key":"1336_CR18","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1080\/02331930410001661505","volume":"53","author":"J Dutta","year":"2004","unstructured":"Dutta, J., Chandra, S.: Convexifcators, generalized convexity and vector optimzation. Optimization 53, 77\u201394 (2004)","journal-title":"Optimization"},{"key":"1336_CR19","first-page":"433","volume":"5","author":"P Michel","year":"1992","unstructured":"Michel, P., Penot, J.P.: A generalized derivative for calm and stable functions. Differ. Integral Equ. 5, 433\u2013454 (1992)","journal-title":"Differ. Integral Equ."},{"key":"1336_CR20","first-page":"211","volume":"2","author":"BS Mordukhovich","year":"1995","unstructured":"Mordukhovich, B.S., Shao, Y.H.: On nonconvex subdifferential calculus in Banach space. J. Convex Anal. 2, 211\u2013227 (1995)","journal-title":"J. Convex Anal."},{"key":"1336_CR21","doi-asserted-by":"publisher","first-page":"670","DOI":"10.1137\/0805033","volume":"5","author":"JS Treiman","year":"1995","unstructured":"Treiman, J.S.: The linear nonconvex generalized gradient and Lagrange multipliers. SIAM J. Optim 5, 670\u2013680 (1995)","journal-title":"SIAM J. Optim"},{"key":"1336_CR22","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s11228-009-0103-6","volume":"17","author":"N Movahedian","year":"2009","unstructured":"Movahedian, N., Nobakhtian, S.: Constraint qualifications for nonsmooth mathematical programs with equilibrium constraints. Set-Valued Var. Anal. 17, 63\u201395 (2009)","journal-title":"Set-Valued Var. Anal."},{"key":"1336_CR23","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s10957-009-9518-3","volume":"142","author":"A Moldovan","year":"2009","unstructured":"Moldovan, A., Pellegrini, L.: On regularity for constrained extremum problems. \n                    \n                      \n                    \n                    $$\\text{ P }$$\n                    \n                      \n                        \n                          \n                          P\n                          \n                        \n                      \n                    \n                  art 1: sufficient optimality conditions. J. Optim. Theory Appl. 142, 147\u2013163 (2009)","journal-title":"J. Optim. Theory Appl."},{"key":"1336_CR24","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/s10957-009-9521-8","volume":"142","author":"A Moldovan","year":"2009","unstructured":"Moldovan, A., Pellegrini, L.: On regularity for constrained extremum problems. \n                    \n                      \n                    \n                    $$\\text{ P }$$\n                    \n                      \n                        \n                          \n                          P\n                          \n                        \n                      \n                    \n                  art 2: necessary optimality conditions. J. Optim. Theory Appl. 142, 165\u2013183 (2009)","journal-title":"J. Optim. Theory Appl."},{"key":"1336_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-64277-2","volume-title":"Variational Analysis of Regular Mappings. Theory and Applications","author":"AD Ioffe","year":"2017","unstructured":"Ioffe, A.D.: Variational Analysis of Regular Mappings. Theory and Applications. Springer, New York (2017)"},{"key":"1336_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-4820-3","volume-title":"Functional Analysis, Calculus of Variations and Optimal Control","author":"F Clarke","year":"2013","unstructured":"Clarke, F.: Functional Analysis, Calculus of Variations and Optimal Control. Springer, London (2013)"},{"key":"1336_CR27","volume-title":"Variational Analysis and Generalized Differentiation I. Basic Theory","author":"BS Mordukhovich","year":"2006","unstructured":"Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation I. Basic Theory. Springer, New York (2006)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-018-1336-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-018-1336-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-018-1336-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,25]],"date-time":"2019-07-25T23:14:06Z","timestamp":1564096446000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-018-1336-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,26]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["1336"],"URL":"https:\/\/doi.org\/10.1007\/s10957-018-1336-z","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7,26]]},"assertion":[{"value":"25 September 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 June 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 July 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}