{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T00:30:45Z","timestamp":1775521845884,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1981,2,1]],"date-time":"1981-02-01T00:00:00Z","timestamp":349833600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Zeitschrift f\u00fcr Operations Research"],"published-print":{"date-parts":[[1981,2]]},"DOI":"10.1007\/bf01917339","type":"journal-article","created":{"date-parts":[[2005,7,30]],"date-time":"2005-07-30T06:56:49Z","timestamp":1122706609000},"page":"15-23","source":"Crossref","is-referenced-by-count":5,"title":["Approximation operators in optimization theory"],"prefix":"10.1007","volume":"25","author":[{"given":"M.","family":"Vlach","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF01917339_CR1","unstructured":"Abadie, J.: On the Kuhn-Tucker Theorem. In Nonlinear Programming. Ed. by. J. Abadie. Amsterdam 1967."},{"key":"BF01917339_CR2","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/BF00935191","volume":"11","author":"M.S. Bazaraa","year":"1975","unstructured":"Bazaraa, M.S., andJ.J. Goode: Necessary optimality criteria in mathematical programming in normed linear spaces. J. Opt. Theory Appl11, 1975, 235\u2013244.","journal-title":"J. Opt. Theory Appl"},{"key":"BF01917339_CR3","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/BF00934938","volume":"13","author":"M.S. Bazaraa","year":"1974","unstructured":"Bazaraa, M.S., J.J. Goode andM.Z. Nashed: On the cones of tangents with applications to mathematical programming. J. Opt. Theory Appl.13, 1974, 389\u2013426.","journal-title":"J. Opt. Theory Appl."},{"key":"BF01917339_CR4","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1080\/00036817608839119","volume":"5","author":"M.S. Bazaraa","year":"1976","unstructured":"Bazaraa, M.S., C.M. Shetty, J.J. Goode andM.Z. Nashed: Nonlinear programming without differentiability in Banach spaces: Necessary and sufficient constraint qualification. Applicable Analysis5, 1976, 165\u2013173.","journal-title":"Applicable Analysis"},{"key":"BF01917339_CR5","unstructured":"Birkhoff, G.: Lattice Theory, 3rd ed. Providence, Rhode Island 1976, p. 111."},{"key":"BF01917339_CR6","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1137\/0316034","volume":"16","author":"J. Borwein","year":"1978","unstructured":"Borwein, J.: Weak tangent cones and optimization in a Banach space. SIAM J. Control and Optimization16, 1978, 512\u2013522.","journal-title":"SIAM J. Control and Optimization"},{"key":"BF01917339_CR7","unstructured":"Bouligand, G.: Introduction \u00e0 la G\u00e9om\u00e9trie infinit\u00e9simale directe. Paris 1932."},{"key":"BF01917339_CR8","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1137\/0304041","volume":"4","author":"M. Canon","year":"1966","unstructured":"Canon, M., C. Cullum andE. Polak: Constrained minimization problems in finite-dimensional spaces. J. SIAM Control4, 1966, 528\u2013547.","journal-title":"J. SIAM Control"},{"key":"BF01917339_CR9","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1090\/S0002-9947-1975-0367131-6","volume":"205","author":"F.H. Clarke","year":"1975","unstructured":"Clarke, F.H.: Generalized gradients and applications. Trans. AMS205, 1975, 247\u2013262.","journal-title":"Trans. AMS"},{"key":"BF01917339_CR10","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1287\/moor.1.2.165","volume":"1","author":"F.H. Clarke","year":"1976","unstructured":"\u2014: A new approach to Lagrange multipliers. Math. of Op. Research1, 1976, 165\u2013174.","journal-title":"Math. of Op. Research"},{"key":"BF01917339_CR11","doi-asserted-by":"crossref","first-page":"D 225","DOI":"10.21136\/CPMF.1937.123380","volume":"66","author":"E. \u010cech","year":"1937","unstructured":"\u010cech, E.: Topologick\u00e9 prostory (Topological Spaces). \u010cas. pro p\u00e8stovani matematiky a fyziky66, 1937, D 225-D 264.","journal-title":"\u010cas. pro p\u00e8stovani matematiky a fyziky"},{"key":"BF01917339_CR12","unstructured":"-: Topologick\u00e9 prostory (Topological Spaces). Prague 1959."},{"key":"BF01917339_CR13","first-page":"406","volume":"2","author":"V.F. Demyanov","year":"1966","unstructured":"Demyanov, V.F., andA.M. Rubinov: On necessary conditions for an extremum. Ekonomika i Matematickeskie Metody2, 1966, 406\u2013417.","journal-title":"Ekonomika i Matematickeskie Metody"},{"key":"BF01917339_CR14","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1137\/0306006","volume":"6","author":"V.F. Demyanov","year":"1968","unstructured":"\u2014: Minimization of functionals in normed spaces. SIAM J. Control6, 1968, 73\u201388.","journal-title":"SIAM J. Control"},{"key":"BF01917339_CR15","first-page":"395","volume":"5","author":"A. Ya. Dubovitskii","year":"1965","unstructured":"Dubovitskii, A. Ya., andA.A. Milyutin: Extremum problems in the presence of restrictions. Zh. Vychisl. Mat. i Mat. Fiz.5, 1965, 395\u2013453.","journal-title":"Zh. Vychisl. Mat. i Mat. Fiz."},{"key":"BF01917339_CR16","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1112\/jlms\/s1-42.1.523","volume":"42","author":"T.M. Flett","year":"1967","unstructured":"Flett, T.M.: On differentiation in normed vector spaces. Journal London Math. Soc.42, 1967, 523\u2013533.","journal-title":"Journal London Math. Soc."},{"key":"BF01917339_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01584534","volume":"2","author":"F.J. Gould","year":"1972","unstructured":"Gould, F.J., andJ.W. Tolle: Geometry of optimality conditions and constraint qualifications. Math. Programming2, 1972, 1\u201318.","journal-title":"Math. Programming"},{"key":"BF01917339_CR18","unstructured":"Hestenes, M.R.: Calculus of Variations and Optimal Control Theory. New York 1966."},{"key":"BF01917339_CR19","unstructured":"-: Optimization Theory: The Finite Dimensional Case. New York 1975."},{"key":"BF01917339_CR20","doi-asserted-by":"crossref","first-page":"57","DOI":"10.24033\/msmf.261","volume":"60","author":"J.B. Hiriart-Urruty","year":"1979","unstructured":"Hiriart-Urruty, J.B.: New concepts in nondifferentiable programming. Journ\u00e9es d'Analyse Non Convexe (Mai 1977), Bull. Soc. Math. France, M\u00e9moire60, 1979, 57\u201385.","journal-title":"Bull. Soc. Math. France, M\u00e9moire"},{"key":"BF01917339_CR21","unstructured":"-: Mean value theorems in nonsmooth analysis. To appear in Numerical Functional Analysis and Optimization."},{"issue":"41","key":"BF01917339_CR22","first-page":"74","volume":"24","author":"A. G. Kusraev","year":"1980","unstructured":"Kusraev, A. G.: Subdifferentiation of nonsmooth operators and the necessary extremum conditions in multicriteria problems with restrictions. Optimizacia24 (41), 1980, 74\u2013117.","journal-title":"Optimizacia"},{"key":"BF01917339_CR23","first-page":"39","volume":"4","author":"I. Lasiecka","year":"1975","unstructured":"Lasiecka, I.: Conical approximations of sets in optimization theory. Control and Cybernetics4, 1975, 39\u201358.","journal-title":"Control and Cybernetics"},{"key":"BF01917339_CR24","unstructured":"Lobry, C.: Etude G\u00e9ometrique des Probl\u00e8mes d'optimisation en presence de constraintes. These, Univ. Grenoble, 1967."},{"key":"BF01917339_CR25","doi-asserted-by":"crossref","unstructured":"Neustadt, L. W.: Optimal Control Problems with Operator Equation Restrictions. In Lecture Notes in Math.,132. Berlin-Heidelberg-New York 1970.","DOI":"10.1007\/BFb0066688"},{"key":"BF01917339_CR26","unstructured":"Rockafellar, R. T.: The Theory of subgradients and its applications to problems of optimization. Lecture Notes, University of Montreal, 1978."},{"key":"BF01917339_CR27","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1080\/02331937808842516","volume":"9","author":"E. Sachs","year":"1978","unstructured":"Sachs, E.: Differentiability in optimization theory. Math. Operationsforsch. Statist., ser. Optimization9, 1978, 497\u2013513.","journal-title":"Math. Operationsforsch. Statist., ser. Optimization"},{"key":"BF01917339_CR28","unstructured":"Saks, S.: Theory of the Integral, second revised edition. New York 1937."},{"key":"BF01917339_CR29","unstructured":"Schwartz, L.: Analyse Math\u00e9matique I. Paris 1967."},{"key":"BF01917339_CR30","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1137\/0115028","volume":"15","author":"P.P. Varaiya","year":"1967","unstructured":"Varaiya, P.P.: Nonlinear Programming in Banach Space. SIAM Appl. Math.15, 1967, 284\u2013293.","journal-title":"SIAM Appl. Math."},{"issue":"3","key":"BF01917339_CR31","first-page":"501","volume":"11","author":"M. Vlach","year":"1970","unstructured":"Vlach, M.: On necessary conditions of optimality in linear spaces. Comm. Math. Univ. Caroline11 (3), 1970, 501\u2013513.","journal-title":"Comm. Math. Univ. Caroline"},{"key":"BF01917339_CR32","unstructured":"-: Dubovitskii \u2014 Milyutin approach to optimization. Mem. no.280, Twente Univ. of Technology, September 1979."},{"key":"BF01917339_CR33","first-page":"251","volume":"37","author":"M. Vlach","year":"1980","unstructured":"\u2014: On the cones of tangents. Methods of Operations Research37, 1980, 251\u2013256.","journal-title":"Methods of Operations Research"},{"key":"BF01917339_CR34","unstructured":"Zoutendijk, G.: Methods of feasible directions. Amsterdam 1960."}],"container-title":["Zeitschrift f\u00fcr Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01917339.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01917339\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01917339","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T07:08:02Z","timestamp":1626246482000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01917339"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1981,2]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1981,2]]}},"alternative-id":["BF01917339"],"URL":"https:\/\/doi.org\/10.1007\/bf01917339","relation":{},"ISSN":["0340-9422","1432-5217"],"issn-type":[{"value":"0340-9422","type":"print"},{"value":"1432-5217","type":"electronic"}],"subject":[],"published":{"date-parts":[[1981,2]]}}}