{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:32:23Z","timestamp":1759847543722},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2013,9,25]],"date-time":"2013-09-25T00:00:00Z","timestamp":1380067200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2014,10]]},"DOI":"10.1007\/s10107-013-0709-1","type":"journal-article","created":{"date-parts":[[2013,9,24]],"date-time":"2013-09-24T07:14:38Z","timestamp":1380006878000},"page":"47-79","source":"Crossref","is-referenced-by-count":3,"title":["Geometric measures of convex sets and bounds on problem sensitivity and robustness for conic linear optimization"],"prefix":"10.1007","volume":"147","author":[{"given":"Jorge R.","family":"Vera","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,9,25]]},"reference":[{"key":"709_CR1","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01758841","volume":"8","author":"I Adler","year":"1992","unstructured":"Adler, I., Monteiro, R.: A geometric view of parametric linear programming. Algorithmica 8, 161\u2013176 (1992)","journal-title":"Algorithmica"},{"issue":"1","key":"709_CR2","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s10107-007-0203-8","volume":"119","author":"A Belloni","year":"2009","unstructured":"Belloni, A., Freund, R.: A geometric analysis of Renegar\u2019s condition number, and its interplay with conic curvature. Math. Program. 119(1), 95\u2013107 (2009)","journal-title":"Math. Program."},{"key":"709_CR3","unstructured":"Ben-Tal, A., Nemirovski, A.: Robust convex optimization. Math. Oper. Res. 23, 769\u2013805 (1998)"},{"key":"709_CR4","doi-asserted-by":"crossref","unstructured":"Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52(1), 3553 (2004)","DOI":"10.1287\/opre.1030.0065"},{"key":"709_CR5","doi-asserted-by":"crossref","unstructured":"Bonnans, J., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, Berlin (2000)","DOI":"10.1007\/978-1-4612-1394-9"},{"key":"709_CR6","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)"},{"key":"709_CR7","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s101070100237","volume":"91","author":"D Cheung","year":"2001","unstructured":"Cheung, D., Cucker, F.: A new condition number for linear programming. Math. Program. 91, 163\u2013174 (2001)","journal-title":"Math. Program."},{"issue":"4","key":"709_CR8","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1287\/moor.28.4.609.20520","volume":"28","author":"D Cheung","year":"2003","unstructured":"Cheung, D., Cucker, F., Pea, J.: Unifying condition numbers for linear programming. Math. Oper. Res. 28(4), 609\u2013624 (2003)","journal-title":"Math. Oper. Res."},{"key":"709_CR9","doi-asserted-by":"crossref","unstructured":"Dantzig, G.: Linear Programming and Extensions. Princeton University Press, Princeton NJ (1963)","DOI":"10.1515\/9781400884179"},{"issue":"2","key":"709_CR10","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1073\/pnas.45.2.223","volume":"45","author":"A Dvorestzky","year":"1959","unstructured":"Dvorestzky, A.: A theorem on convex bodies and applications to Banach spaces. Proc. Natl. Acad. Sci. 45(2), 223\u2013226 (1959)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"709_CR11","doi-asserted-by":"crossref","unstructured":"Eggleston, H.G.: Convexity. Cambridge University Press, Cambridge (1958), reprinted 2008","DOI":"10.1017\/CBO9780511566172"},{"key":"709_CR12","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1137\/S0895479896298130","volume":"18","author":"L Ghaoui El","year":"1997","unstructured":"El Ghaoui, L., Lebret, H.: Robust solutions to least-square problems to uncertain data matrices. SIAM J. Matrix Anal. Appl. 18, 1035\u20131064 (1997)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"709_CR13","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1137\/S1052623400373829","volume":"12","author":"M Epelman","year":"2002","unstructured":"Epelman, M., Freund, R.: A new condition measure, preconditioners and relations between different measures of conditioning for conic linear systems. SIAM J. Optim. 12, 627\u2013655 (2002)","journal-title":"SIAM J. Optim."},{"key":"709_CR14","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1137\/S1052623401393645","volume":"13","author":"R Freund","year":"2003","unstructured":"Freund, R.: On the primal-dual geometry of level sets in linear and conic optimization. SIAM J. Optim. 13, 1004\u20131013 (2003)","journal-title":"SIAM J. Optim."},{"key":"709_CR15","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1137\/S105262349732829X","volume":"10","author":"R Freund","year":"1999","unstructured":"Freund, R., Vera, J.: Condition-based complexity of convex optimization in conic form via the ellipsod algorithm. SIAM J. Optim. 10, 155\u2013176 (1999)","journal-title":"SIAM J. Optim."},{"key":"709_CR16","unstructured":"Freund, R., Vera, J.: On the complexity of computing estimates of condition measures of a conic linear system. Math. Oper. Res. 28(4), 625\u2013648 (2003)"},{"issue":"4","key":"709_CR17","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1287\/moor.1090.0408","volume":"34","author":"R Freund","year":"2009","unstructured":"Freund, R., Vera, J.: Equivalence of convex problem geometry and computational complexity in the separation oracle model. Math. Oper. Res. 34(4), 869\u2013879 (2009)","journal-title":"Math. Oper. Res."},{"key":"709_CR18","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF02055197","volume":"27","author":"J Gauvin","year":"1990","unstructured":"Gauvin, J., Janin, R.: Directional derivative of the value function in parametric optimization. Ann. Oper. Res. 27, 237\u2013252 (1990)","journal-title":"Ann. Oper. Res."},{"key":"709_CR19","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1137\/S1052623402401579","volume":"14","author":"M Goberna","year":"2003","unstructured":"Goberna, M., L\u00f3pez, M., Todorov, M.: Extended active constraints in linear optimization with applications. SIAM J. Optim. 14, 608\u2013619 (2003)","journal-title":"SIAM J. Optim."},{"key":"709_CR20","unstructured":"Iusem, A., Seeger, A.: Computing the radius of pointedness of a convex cone. Math. Program. Ser. B 111, 217\u2013241 (2008)"},{"key":"709_CR21","unstructured":"Kall, P., Mayer, J.: Stochastic Linear Programming: Models, Theory and Computation. Kluwer, Dordrecht (2005)"},{"issue":"2","key":"709_CR22","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1287\/opre.43.2.264","volume":"43","author":"JM Mulvey","year":"1995","unstructured":"Mulvey, J.M., Vanderbei, R., Zenios, S.: Robust optimization of large-scale systems. Oper. Res. 43(2), 264\u2013281 (1995)","journal-title":"Oper. Res."},{"issue":"1","key":"709_CR23","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF02592332","volume":"72","author":"R Monteiro","year":"1996","unstructured":"Monteiro, R., Mehrotra, S.: A general parametric analysis approach and its implication to sensitivity analysis in interior point methods. Math. Program. 72(1), 65\u201382 (1996)","journal-title":"Math. Program."},{"key":"709_CR24","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/BF01581642","volume":"19","author":"KG Murty","year":"1980","unstructured":"Murty, K.G.: Computational complexity of parametric linear programming. Math. Program. 19, 213\u2013219 (1980)","journal-title":"Math. Program."},{"issue":"2","key":"709_CR25","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1137\/S1052623402401804","volume":"14","author":"F Ord\u00f3\u00f1ez","year":"2003","unstructured":"Ord\u00f3\u00f1ez, F., Freund, R.: Computational experience and the explanatory value of condition measures for linear optimization. SIAM J. Opt. 14(2), 337\u2013333 (2003)","journal-title":"SIAM J. Opt."},{"issue":"3","key":"709_CR26","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1137\/0805026","volume":"5","author":"J Renegar","year":"1995","unstructured":"Renegar, J.: Incorporating condition measures into the complexity theory of linear programming. SIAM J. Optim. 5(3), 506\u2013524 (1995)","journal-title":"SIAM J. Optim."},{"key":"709_CR27","doi-asserted-by":"crossref","unstructured":"Shapiro, A.: On duality theory of conic linear problems. In: Shapiro, A. (ed.) Semi-Infinite Programming, pp. 135\u2013165. Kluwer, Dordrecht (2000)","DOI":"10.1007\/978-1-4757-3403-4_7"},{"key":"709_CR28","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.1287\/opre.21.5.1154","volume":"21","author":"A Soyster","year":"1973","unstructured":"Soyster, A.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21, 1154\u20131157 (1973)","journal-title":"Oper. Res."},{"key":"709_CR29","unstructured":"Vera, J.: Ill-Posedness in Mathematica Programming and Problem Solving with Approximate Data, Ph.D. Thesis, Cornell University (1992)"},{"key":"709_CR30","unstructured":"Werner, R.: Consistency of Robust Optimization with Applications to Portfolio Optimization. Working Paper"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-013-0709-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-013-0709-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-013-0709-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,25]],"date-time":"2019-07-25T02:00:11Z","timestamp":1564020011000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-013-0709-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,25]]},"references-count":30,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["709"],"URL":"https:\/\/doi.org\/10.1007\/s10107-013-0709-1","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9,25]]}}}