{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T13:55:09Z","timestamp":1676382909136},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,9,5]],"date-time":"2017-09-05T00:00:00Z","timestamp":1504569600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2017,11]]},"DOI":"10.1007\/s10957-017-1164-6","type":"journal-article","created":{"date-parts":[[2017,9,5]],"date-time":"2017-09-05T19:19:22Z","timestamp":1504639162000},"page":"567-589","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Stability and Solution Sensitivity of a Consumer Problem"],"prefix":"10.1007","volume":"175","author":[{"given":"Vu Thi","family":"Huong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jen-Chih","family":"Yao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nguyen Dong","family":"Yen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,9,5]]},"reference":[{"key":"1164_CR1","volume-title":"Mathematical Economics","author":"A Takayama","year":"1974","unstructured":"Takayama, A.: Mathematical Economics. The Dryden Press, Hinsdale (1974)"},{"key":"1164_CR2","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719215","volume-title":"Mathematical Optimization and Economic Theory","author":"MD Intriligator","year":"2002","unstructured":"Intriligator, M.D.: Mathematical Optimization and Economic Theory, 2nd edn. SIAM, Philadelphia (2002)","edition":"2"},{"key":"1164_CR3","volume-title":"Fundamental Methods of Mathematical Economics","author":"AC Chiang","year":"2005","unstructured":"Chiang, A.C., Wainwright, K.: Fundamental Methods of Mathematical Economics, 4th edn. McGraw-Hill, New York (2005)","edition":"4"},{"key":"1164_CR4","volume-title":"Microeconomic Theory: Basic Principles and Extension","author":"W Nicholson","year":"2012","unstructured":"Nicholson, W., Snyder, C.: Microeconomic Theory: Basic Principles and Extension, 7th edn. South-Western, Cengage Learning, Boston (2012)","edition":"7"},{"key":"1164_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-30200-8","volume-title":"Production Economics: The Basic Theory of Production. Optimization","author":"S Rasmussen","year":"2013","unstructured":"Rasmussen, S.: Production Economics: The Basic Theory of Production. Optimization, 2nd edn. Springer, Berlin (2013)","edition":"2"},{"key":"1164_CR6","doi-asserted-by":"crossref","first-page":"3619","DOI":"10.1016\/j.apm.2014.11.059","volume":"39","author":"F Jarrahi","year":"2015","unstructured":"Jarrahi, F., Abdul-Kader, W.: Performance evaluation of a multi-product production line: an approximation method. Appl. Math. Model. 39, 3619\u20133636 (2015)","journal-title":"Appl. Math. Model."},{"key":"1164_CR7","doi-asserted-by":"crossref","first-page":"6359","DOI":"10.1016\/j.apm.2015.01.037","volume":"39","author":"GA Keskin","year":"2015","unstructured":"Keskin, G.A., Omurca, S.I., Aydin, N., Ekinci, E.: A comparative study of production-inventory model for determining effective production quantity and safety stock level. Appl. Math. Model. 39, 6359\u20136374 (2015)","journal-title":"Appl. Math. Model."},{"key":"1164_CR8","first-page":"247","volume":"19","author":"K Miyagishima","year":"2015","unstructured":"Miyagishima, K.: Implementability and equity in production economies with unequal skills. Rev. Econ. Des. 19, 247\u2013257 (2015)","journal-title":"Rev. Econ. Des."},{"key":"1164_CR9","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1007\/s10957-013-0289-5","volume":"159","author":"J-P Penot","year":"2013","unstructured":"Penot, J.-P.: Variational analysis for the consumer theory. J. Optim. Theory Appl. 159, 769\u2013794 (2013)","journal-title":"J. Optim. Theory Appl."},{"key":"1164_CR10","first-page":"1071","volume":"15","author":"J-P Penot","year":"2014","unstructured":"Penot, J.-P.: Some properties of the demand correspondence in the consumer theory. J. Nonlinear Convex Anal. 15, 1071\u20131085 (2014)","journal-title":"J. Nonlinear Convex Anal."},{"key":"1164_CR11","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/s10479-013-1507-0","volume":"233","author":"Y-C Tsao","year":"2015","unstructured":"Tsao, Y.-C.: A piecewise nonlinear optimization for a production-inventory model under maintenance, variable setup costs, and trade credits. Ann. Oper. Res. 233, 465\u2013481 (2015)","journal-title":"Ann. Oper. Res."},{"key":"1164_CR12","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s10957-007-9256-3","volume":"134","author":"BK Ane","year":"2007","unstructured":"Ane, B.K., Tarasyev, A.M., Watanabe, C.: Construction of nonlinear stabilizer for trajectories of economic growth. J. Optim. Theory Appl. 134, 303\u2013320 (2007)","journal-title":"J. Optim. Theory Appl."},{"key":"1164_CR13","doi-asserted-by":"crossref","unstructured":"Aseev, S.M., Kryazhimskii, A.V.: The Pontryagin maximum principle and problems of optimal economic growth, translation in Mat. Inst. Steklova. 257 (2007); translation in Proc. Steklov Inst. Math. 257 (2007)\u00a0(in Russian)","DOI":"10.1134\/S0081543807020010"},{"issue":"suppl. 1","key":"1164_CR14","doi-asserted-by":"crossref","first-page":"S143","DOI":"10.1134\/S0081543810050111","volume":"268","author":"AA Krasovskii","year":"2010","unstructured":"Krasovskii, A.A., Tarasyev, A.M.: Construction of nonlinear regulators in economic growth models. Proc. Steklov Inst. Math. 268(suppl. 1), S143\u2013S154 (2010)","journal-title":"Proc. Steklov Inst. Math."},{"key":"1164_CR15","doi-asserted-by":"crossref","first-page":"2495","DOI":"10.1080\/02331934.2015.1080701","volume":"64","author":"N Hadjisavvas","year":"2015","unstructured":"Hadjisavvas, N., Penot, J.-P.: Revisiting the problem of integrability in utility theory. Optimization 64, 2495\u20132509 (2015)","journal-title":"Optimization"},{"key":"1164_CR16","doi-asserted-by":"publisher","unstructured":"Beggs, A.: Sensitivity analysis of boundary equilibria. Econ. Theory. doi: 10.1007\/s00199-016-0987-y (2016)","DOI":"10.1007\/s00199-016-0987-y"},{"key":"1164_CR17","unstructured":"Diewert, W.E.: Applications of duality theory. In: Frontiers of Quantitative Economics, vol. II, pp. 106\u2013206. North-Holland, Amsterdam (1974)"},{"key":"1164_CR18","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/0304-4068(83)90010-1","volume":"12","author":"J-P Crouzeix","year":"1983","unstructured":"Crouzeix, J.-P.: Duality between direct and indirect utility functions. Differentiability properties. J. Math. Econ. 12, 149\u2013165 (1983)","journal-title":"J. Math. Econ."},{"key":"1164_CR19","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/BF01212921","volume":"3","author":"J-E Mart\u00ednez-Legaz","year":"1993","unstructured":"Mart\u00ednez-Legaz, J.-E., Santos, M.S.: Duality between direct and indirect preferences. Econ. Theory 3, 335\u2013351 (1993)","journal-title":"Econ. Theory"},{"key":"1164_CR20","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/BF00938588","volume":"48","author":"JM Borwein","year":"1986","unstructured":"Borwein, J.M.: Stability and regular points of inequality systems. J. Optim. Theory Appl. 48, 9\u201352 (1986)","journal-title":"J. Optim. Theory Appl."},{"key":"1164_CR21","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/BF01215992","volume":"31","author":"ND Yen","year":"1995","unstructured":"Yen, N.D.: H\u00f6lder continuity of solutions to a parametric variational inequality. Appl. Math. Optim. 31, 245\u2013255 (1995)","journal-title":"Appl. Math. Optim."},{"key":"1164_CR22","doi-asserted-by":"crossref","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":"1164_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-31247-1","volume-title":"Variational Analysis and Generalized Differentiation (Vol. I. Basic Theory, Vol. II. Applications)","author":"BS Mordukhovich","year":"2006","unstructured":"Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation (Vol. I. Basic Theory, Vol. II. Applications). Springer, Berlin (2006)"},{"key":"1164_CR24","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1287\/moor.9.1.87","volume":"9","author":"J-P Aubin","year":"1984","unstructured":"Aubin, J.-P.: Lipschitz behavior of solutions to convex minimization problems. Math. Oper. Res. 9, 87\u2013111 (1984)","journal-title":"Math. Oper. Res."},{"key":"1164_CR25","first-page":"17","volume":"12","author":"ND Yen","year":"1987","unstructured":"Yen, N.D.: Implicit function theorems for set-valued maps. Acta Math. Vietnam. 12, 17\u201328 (1987)","journal-title":"Acta Math. Vietnam."},{"key":"1164_CR26","volume-title":"Optimization and Nonsmooth Analysis","author":"FH Clarke","year":"2002","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis, 2nd edn. McGraw-Hill, SIAM, Philadelphia (2002)","edition":"2"},{"key":"1164_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-4848-0","volume-title":"Set-Valued Analysis","author":"JP Aubin","year":"2009","unstructured":"Aubin, J.P., Frankowska, H.: Set-Valued Analysis. Birkh\u00e4user, Boston (2009). (reprint of the 1990 edition)"},{"key":"1164_CR28","unstructured":"Gfrerer, H., Mordukhovich, B.S.: Robinson stability of parametric constraint systems via variational analysis. Preprint, July 26 (2016)"},{"key":"1164_CR29","volume-title":"Functional Analysis","author":"W Rudin","year":"1991","unstructured":"Rudin, W.: Functional Analysis, 2nd edn. McGraw-Hill Inc, New York (1991)","edition":"2"},{"key":"1164_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-70914-7","volume-title":"Functional Analysi Sobolev Spaces and Partial Differential Equations","author":"H Brezis","year":"2011","unstructured":"Brezis, H.: Functional Analysi Sobolev Spaces and Partial Differential Equations. Springer, New York (2011)"},{"key":"1164_CR31","doi-asserted-by":"crossref","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":"1164_CR32","doi-asserted-by":"crossref","first-page":"986","DOI":"10.1137\/140998469","volume":"26","author":"DTK Huyen","year":"2016","unstructured":"Huyen, D.T.K., Yen, N.D.: Coderivatives and the solution map of a linear constraint system. SIAM J. Optim. 26, 986\u20131007 (2016)","journal-title":"SIAM J. Optim."},{"key":"1164_CR33","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/A:1022662120550","volume":"93","author":"ND Yen","year":"1997","unstructured":"Yen, N.D.: Stability of the solution set of perturbed nonsmooth inequality systems and application. J. Optim. Theory Appl. 93, 199\u2013225 (1997)","journal-title":"J. Optim. Theory Appl."},{"key":"1164_CR34","volume-title":"Numerical Methods for Solving Extremal Problems","author":"FP Vasilev","year":"1988","unstructured":"Vasilev, F.P.: Numerical Methods for Solving Extremal Problems, 2nd edn. Nauka, Moscow (1988). (in Russian)","edition":"2"},{"key":"1164_CR35","volume-title":"An Introduction to Variational Inequalities and Their Applications","author":"D Kinderlehrer","year":"1980","unstructured":"Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications. Academic Press, New York (1980)"},{"key":"1164_CR36","volume-title":"Handbook of Generalized Convexity and Generalized Monotonicity","year":"2005","unstructured":"Hadjisavvas, N., Koml\u00f3si, S., Schaible, S. (eds.): Handbook of Generalized Convexity and Generalized Monotonicity. Springer, New York (2005)"},{"key":"1164_CR37","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1287\/moor.19.3.691","volume":"19","author":"J-C Yao","year":"1994","unstructured":"Yao, J.-C.: Variational inequalities with generalized monotone operators. Math. Oper. Res. 19, 691\u2013705 (1994)","journal-title":"Math. Oper. Res."},{"key":"1164_CR38","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/BF02196593","volume":"80","author":"J-C Yao","year":"1994","unstructured":"Yao, J.-C.: Multi-valued variational inequalities with K-pseudomonotone operators. J. Optim. Theory Appl. 80, 63\u201374 (1994)","journal-title":"J. Optim. Theory Appl."},{"key":"1164_CR39","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/0-387-23393-8_12","volume-title":"Handbook of Generalized Convexity and Generalized Monotonicity","author":"J-C Yao","year":"2005","unstructured":"Yao, J.-C., Chadli, O.: Pseudomonotone complementarity problems and variational in equalities. In: Hadjisavvas, N., Koml\u00f3si, S., Schaible, S. (eds.) Handbook of Generalized Convexity and Generalized Monotonicity, pp. 501\u2013558. Springer, Berlin (2005)"},{"key":"1164_CR40","volume-title":"Managerial Economics. Theory, Applications, and Cases","author":"WB Allen","year":"2005","unstructured":"Allen, W.B., Doherty, N.A., Weigelt, K., Mansfield, E.: Managerial Economics. Theory, Applications, and Cases, 6th edn. W. W. Norton and Company, New York (2005)","edition":"6"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-017-1164-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-017-1164-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-017-1164-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,2]],"date-time":"2022-08-02T06:40:49Z","timestamp":1659422449000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-017-1164-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,5]]},"references-count":40,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,11]]}},"alternative-id":["1164"],"URL":"https:\/\/doi.org\/10.1007\/s10957-017-1164-6","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,5]]}}}