{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T18:34:04Z","timestamp":1781202844405,"version":"3.54.1"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,1,15]],"date-time":"2008-01-15T00:00:00Z","timestamp":1200355200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2008,9]]},"DOI":"10.1007\/s10898-007-9270-x","type":"journal-article","created":{"date-parts":[[2008,1,14]],"date-time":"2008-01-14T06:23:32Z","timestamp":1200291812000},"page":"121-138","source":"Crossref","is-referenced-by-count":23,"title":["An inexact proximal point method for solving generalized fractional programs"],"prefix":"10.1007","volume":"42","author":[{"given":"Jean-Jacques","family":"Strodiot","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Pierre","family":"Crouzeix","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jacques A.","family":"Ferland","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Van Hien","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2008,1,15]]},"reference":[{"key":"9270_CR1","unstructured":"Birbil, S.I., Frenk, J.B., Zhang, S.: Generalized fractional programming with user interaction. ERIM Report Series Research in Management ERS-2004-033-LIS (2004)"},{"key":"9270_CR2","volume-title":"Optimization and Nonsmooth Analysis","author":"F.H. Clarke","year":"1983","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)"},{"key":"9270_CR3","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/BF01585170","volume":"62","author":"R. Correa","year":"1993","unstructured":"Correa, R., Lemar\u00e9chal, C.: Convergence of some algorithms for convex minimization. Math. Program. 62, 261\u2013275 (1993)","journal-title":"Math. Program."},{"key":"9270_CR4","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/BF00941314","volume":"47","author":"J.P. Crouzeix","year":"1985","unstructured":"Crouzeix, J.P., Ferland, J.A., Schaible, S.: An algorithm for generalized fractional programs. J. Optim. Theory Appl. 47, 35\u201349 (1985)","journal-title":"J. Optim. Theory Appl."},{"key":"9270_CR5","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/BF00938484","volume":"50","author":"J.P. Crouzeix","year":"1986","unstructured":"Crouzeix, J.P., Ferland, J.A., Schaible, S.: A note on an algorithm for generalized fractional programs. J. Optim. Theory Appl. 50, 183\u2013187 (1986)","journal-title":"J. Optim. Theory Appl."},{"key":"9270_CR6","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1137\/S1052623402411459","volume":"14","author":"A. Fuduli","year":"2004","unstructured":"Fuduli, A., Gaudioso, M., Giallombardo, G.: Minimizing nonconvex nonsmooth functions via cutting planes and proximity control. SIAM J. Optim. 14, 743\u2013756 (2004)","journal-title":"SIAM J. Optim."},{"key":"9270_CR7","doi-asserted-by":"crossref","first-page":"1493","DOI":"10.1287\/mnsc.42.10.1493","volume":"42","author":"M. Gugat","year":"1996","unstructured":"Gugat, M.: A fast algorithm for a class of generalized fractional programs. Manage. Sci. 42, 1493\u20131499 (1996)","journal-title":"Manage. Sci."},{"key":"9270_CR8","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1023\/A:1021759318653","volume":"99","author":"M. Gugat","year":"1998","unstructured":"Gugat, M.: Prox-regularization methods for generalized fractional programming. J. Optim. Theory Appl. 99, 691\u2013722 (1998)","journal-title":"J. Optim. Theory Appl."},{"key":"9270_CR9","doi-asserted-by":"crossref","unstructured":"Hare, W., Sagastiz\u00e1bal, C.: Computing proximal points of nonconvex functions. Math. Program. Ser. B (2007). doi: 10.1007\/s10107-007-0124-6","DOI":"10.1007\/s10107-007-0124-6"},{"key":"9270_CR10","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1023\/B:JOTA.0000026134.57920.e1","volume":"121","author":"T.T. Hue","year":"2004","unstructured":"Hue, T.T., Strodiot, J.J., Nguyen, V.H.: Convergence of the approximate auxiliary problem method for solving generalized variational inequalities. J. Optim. Theory Appl. 121, 119\u2013145 (2004)","journal-title":"J. Optim. Theory Appl."},{"key":"9270_CR11","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1023\/A:1008321423879","volume":"13","author":"A. Kaplan","year":"1998","unstructured":"Kaplan, A., Tichatschke, R.: Proximal point methods and nonconvex optimization. J. Global Optim. 13, 389\u2013406 (1998)","journal-title":"J. Global Optim."},{"key":"9270_CR12","first-page":"245","volume-title":"Nonlinear Programming, vol. 4","author":"C. Lemar\u00e9chal","year":"1981","unstructured":"Lemar\u00e9chal, C., Strodiot, J.J., Bihain, A.: On a bundle method for nonsmooth optimization. In: Mangasarian, O., Meyer, R., Robinson, S.(eds) Nonlinear Programming, vol. 4, pp. 245\u2013282. Academic Press, New York (1981)"},{"key":"9270_CR13","first-page":"154","volume":"4","author":"B. Martinet","year":"1970","unstructured":"Martinet, B.: R\u00e9gularisation d\u2019in\u00e9quations variationelles par approximations successives. RAIRO Rech. Oper. 4, 154\u2013159 (1970)","journal-title":"RAIRO Rech. Oper."},{"key":"9270_CR14","doi-asserted-by":"crossref","unstructured":"Nguyen, T.T.V., Strodiot, J.J., Nguyen, V.H.: A bundle method for solving equilibrium problems. Math. Program. Ser. B (2007). doi: 10.1007\/s10107-007-0112-x","DOI":"10.1007\/s10107-007-0112-x"},{"key":"9270_CR15","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/0314056","volume":"14","author":"R.T. Rockafellar","year":"1976","unstructured":"Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14, 877\u2013898 (1976)","journal-title":"SIAM J. Control Optim."},{"key":"9270_CR16","volume-title":"Variational Analysis. No. 317 in Grundlehren der Mathematischen Wissenschaften","author":"R.T. Rockafellar","year":"1998","unstructured":"Rockafellar, R.T., Wets, R.B.: Variational Analysis. No. 317 in Grundlehren der Mathematischen Wissenschaften. Springer, Heidelberg (1998)"},{"key":"9270_CR17","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1051\/ro:2002006","volume":"36","author":"A. Roubi","year":"2002","unstructured":"Roubi, A.: Convergence of prox-regularization methods for generalized fractional programming. RAIRO Rech. Oper. 36, 73\u201394 (2002)","journal-title":"RAIRO Rech. Oper."},{"key":"9270_CR18","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1137\/S1052623401384096","volume":"14","author":"G. Salmon","year":"2004","unstructured":"Salmon, G., Strodiot, J.J., Nguyen, V.H.: A bundle method for solving variational inequalities. SIAM J. Optim. 14, 869\u2013893 (2004)","journal-title":"SIAM J. Optim."},{"key":"9270_CR19","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1023\/B:JOTA.0000037605.19435.63","volume":"121","author":"R.L. Sheu","year":"2004","unstructured":"Sheu, R.L., Lin, J.Y.: Solving continuous min-max problems by an iterative entropic regularization method. J. Optim. Theory Appl. 121, 597\u2013612 (2004)","journal-title":"J. Optim. Theory Appl."},{"key":"9270_CR20","volume-title":"Topics in Nonsmooth Mechanics","author":"J.J. Strodiot","year":"1988","unstructured":"Strodiot, J.J., Nguyen, V.H.: On the numerical treatment of the inclusion 0 \u03f5 \u2202 f ( x). In: Moreau, J.J., Panagiotopoulos, P.D., Strang, G.(eds) Topics in Nonsmooth Mechanics, Birk\u00e4user Verlag, Basel (1988)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-007-9270-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-007-9270-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-007-9270-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T08:12:10Z","timestamp":1559290330000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-007-9270-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,15]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,9]]}},"alternative-id":["9270"],"URL":"https:\/\/doi.org\/10.1007\/s10898-007-9270-x","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1,15]]}}}