{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T22:32:07Z","timestamp":1757457127424},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[1992,10,1]],"date-time":"1992-10-01T00:00:00Z","timestamp":717897600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[1992,10]]},"DOI":"10.1007\/bf02139477","type":"journal-article","created":{"date-parts":[[2005,9,15]],"date-time":"2005-09-15T16:33:56Z","timestamp":1126802036000},"page":"409-436","source":"Crossref","is-referenced-by-count":22,"title":["A cutting plane method for solving minimax problems in the complex plane"],"prefix":"10.1007","volume":"2","author":[{"given":"Rembert","family":"Reemtsen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,12,27]]},"reference":[{"key":"BF02139477_CR1","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/BFb0067692","volume-title":"Numerical Analysis","author":"I. Barrodale","year":"1978","unstructured":"I. Barrodale, Best approximation of complex-valued data, in:Numerical Analysis, ed. G.A. Watson (Springer, Berlin\/Heidelberger\/New York, 1978) pp. 14\u201322."},{"key":"BF02139477_CR2","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1090\/S0025-5718-1978-0483298-X","volume":"32","author":"I. Barrodale","year":"1978","unstructured":"I. Barrodale, L.M. Delves and J.C. Mason, Linear Chebyshev approximation of complex-valued functions, Math. Comp. 32 (1978) 853\u2013863.","journal-title":"Math. Comp."},{"key":"BF02139477_CR3","series-title":"Lecture Notes in Pure and Applied Mathematics","first-page":"113","volume-title":"Optimization: Theory and Applications","author":"H.-P. Blatt","year":"1983","unstructured":"H.-P. Blatt, U. Kaiser and B. Ruffer-Beedgen, A multiple exchange algorithm in convex programming, in:Optimization: Theory and Applications, eds. J.-B. Hiriart-Urruty, W. Oettli and J. Stoer, Lecture Notes in Pure and Applied Mathematics, vol. 86 (Marcel Dekker, New York\/Basel, 1983) pp. 113\u2013130."},{"key":"BF02139477_CR4","volume-title":"Introduction to Approximation Theory","author":"E.W. Cheney","year":"1986","unstructured":"E.W. Cheney,Introduction to Approximation Theory, 2nd ed. (Chelsea, New York, 1986).","edition":"2nd ed."},{"key":"BF02139477_CR5","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/BF01386389","volume":"1","author":"E.W. Cheney","year":"1959","unstructured":"E.W. Cheney and A.A. Goldstein, Newton's method for convex programming and Tchebycheff approximation, Numer. Math. 1 (1959) 253\u2013268.","journal-title":"Numer. Math."},{"key":"BF02139477_CR6","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1090\/S0025-5718-1981-0616366-X","volume":"37","author":"C.B. Dunham","year":"1981","unstructured":"C.B. Dunham and J. Williams, Rate of convergence of discretization in Chebyshev approximation, Math. Comp. 37 (1981) 135\u2013139.","journal-title":"Math. Comp."},{"key":"BF02139477_CR7","first-page":"35","volume":"30","author":"S.W. Ellacott","year":"1976","unstructured":"S.W. Ellacott and J. Williams, Linear Chebyshev approximation in the complex plane using Lawson's algorithm, Math. Comp. 30 (1976) 35\u201344.","journal-title":"Math. Comp."},{"key":"BF02139477_CR8","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1090\/S0025-5718-1981-0595055-4","volume":"36","author":"K. Glashoff","year":"1981","unstructured":"K. Glashoff and K. Roleff, A new method for Chebyshev approximation of complex-valued functions, Math. Comp. 36 (1981) 233\u2013239.","journal-title":"Math. Comp."},{"key":"BF02139477_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02591962","volume":"27","author":"D. Goldfarb","year":"1983","unstructured":"D. Goldfarb and A. Idnani, A numerically stable dual method for solving strictly convex quadratic programs, Math. Progr. 27 (1983) 1\u201333.","journal-title":"Math. Progr."},{"key":"BF02139477_CR10","unstructured":"G.M. Gramlich, SQP-Methoden f\u00fcr semiinfinite Optimierungsprobleme, Ph.D. Thesis, Fachbereich Mathematik, Universit\u00e4t Trier (April 1990)."},{"key":"BF02139477_CR11","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1090\/S0025-5718-1982-0669652-2","volume":"39","author":"U. Grothkopf","year":"1982","unstructured":"U. Grothkopf and G. Opfer, Complex Chebyshev polynomials on circular sectors with degree six or less, Math. Comp. 39 (1982) 599\u2013615.","journal-title":"Math. Comp."},{"key":"BF02139477_CR12","unstructured":"M.H. Gutknecht, Ein Abstiegsverfahren f\u00fcr gleichm\u00e4ssige Approximation, mit Anwendungen, Ph.D. Thesis, Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich (1973)."},{"key":"BF02139477_CR13","doi-asserted-by":"crossref","unstructured":"M.H. Gutknecht, Ein Abstiegsverfahren f\u00fcr nicht-diskrete Tschebyscheff-Approximationsprobleme, in:Numerische Methoden der Approximationstheorie, vol. 4, eds. L. Collatz, G. Meinardus and H. Werner (Birkh\u00e4user, 1978) pp. 154\u2013171.","DOI":"10.1007\/978-3-0348-6460-2_10"},{"key":"BF02139477_CR14","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/0021-9045(78)90110-7","volume":"23","author":"M.H. Gutknecht","year":"1978","unstructured":"M.H. Gutknecht, Non-strong uniqueness in real and complex Chebyshev approximation, J. Approx. Theory 23 (1978) 204\u2013213.","journal-title":"J. Approx. Theory"},{"key":"BF02139477_CR15","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0377-0427(86)90138-X","volume":"14","author":"M. Hartmann","year":"1986","unstructured":"M. Hartmann and G. Opfer, Uniform approximation as a numerical tool for constructing conformal maps, J. Comput. Appl. Math. 14 (1986) 193\u2013206.","journal-title":"J. Comput. Appl. Math."},{"key":"BF02139477_CR16","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1007\/BF01582235","volume":"34","author":"R. Hettich","year":"1986","unstructured":"R. Hettich, An implementation of a discretization method for semi-infinite programming, Math. Progr. 34 (1986) 354\u2013361.","journal-title":"Math. Progr."},{"key":"BF02139477_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-322-93108-5","volume-title":"Numerische Methoden der Approximation und semi-infiniten Optimierung","author":"R. Hettich","year":"1982","unstructured":"R. Hettich and P. Zencke,Numerische Methoden der Approximation und semi-infiniten Optimierung, (B. G. Teubner, Stuttgart, 1982)."},{"key":"BF02139477_CR18","volume-title":"Polynomiale und rationale Tschebyscheff-Approximation in der komplexen Ebene","author":"V. Klotz","year":"1974","unstructured":"V. Klotz, Polynomiale und rationale Tschebyscheff-Approximation in der komplexen Ebene, Ph. D. Thesis, Friedrich-Alexander-Universit\u00e4t, Erlangen-N\u00fcrnberg (1974)."},{"key":"BF02139477_CR19","unstructured":"K.O. Kortanek and Hoon No, A central cutting plane algorithm for convex semi-infinite programming problems, Working Paper Series No. 90-08, College of Business Administration, The University of Iowa, Iowa City, Iowa (revised February 1992)."},{"key":"BF02139477_CR20","first-page":"T208","volume":"55","author":"W. Krabs","year":"1975","unstructured":"W. Krabs and G. Opfer, Eine Methode zur L\u00f6sung des komplexen Approximationsproblems mit einer Anwendung auf konforme Abbildungen. ZAMM 55 (1975) T208-T211.","journal-title":"ZAMM"},{"key":"BF02139477_CR21","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/BF01386060","volume":"6","author":"B.R. Kripke","year":"1964","unstructured":"B.R. Kripke, Best approximation with respect to nearby norms, Numer. Math. 6 (1964) 103\u2013105.","journal-title":"Numer. Math."},{"key":"BF02139477_CR22","first-page":"377","volume":"12","author":"P.J. Laurent","year":"1978","unstructured":"P.J. Laurent and C. Carasso, An algorithm of successive minimization in convex programming, R.A.I.R.O., Analyse num\u00e9rique, Numer. Anal. 12 (1978) 377\u2013400.","journal-title":"Numer. Anal."},{"key":"BF02139477_CR23","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1137\/0317052","volume":"17","author":"O.L. Mangasarian","year":"1979","unstructured":"O.L. Mangasarian and R.R. Meyer, Nonlinear perturbation of linear programs, SIAM J. Control Optim. 17 (1979) 745\u2013752.","journal-title":"SIAM J. Control Optim."},{"key":"BF02139477_CR24","first-page":"471","volume-title":"Approximation Theory V","author":"J.C. Mason","year":"1986","unstructured":"J.C. Mason and G. Opfer, An algorithm for complex polynomial approximation with nonlinear constraints, in:Approximation Theory V, eds. C.K. Chu, L. Schumaker and J. Ward (Academic Press, New York, 1986) pp. 471\u2013474."},{"key":"BF02139477_CR25","unstructured":"J.C. Mason and P. Owen, Some simple algorithms for constrained complex and rational approximation, in:Algorithms for Approximation, eds. J.C. Mason and M.G. Cox (Clarendon Press, 1987) pp. 357\u2013369."},{"key":"BF02139477_CR26","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1007\/978-1-4899-3442-0_37","volume-title":"Algorithms for Approximation II","author":"J.C. Mason","year":"1990","unstructured":"J.C. Mason and S.J. Wilde, Constrained complex approximation algorithms in communication engineering, in:Algorithms for Approximation II, eds. J.C. Mason and M.G. Cox (Chapman and Hill, London\/New York, 1990) pp. 424\u2013448."},{"key":"BF02139477_CR27","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1007\/978-1-4899-3442-0_40","volume-title":"Algorithms for Approximation II","author":"J.C. Mason","year":"1990","unstructured":"J.C. Mason and S.J. Wilde, A complex minimax algorithm for phase-only adaptation in antenna arrays, in:Algorithms for Approximation II, eds. J.C. Mason, and M.G. Cox (Chapman and Hill, London\/New York, 1990) pp. 466\u2013475."},{"key":"BF02139477_CR28","series-title":"Technical Note COMAG 1\/87","volume-title":"Constrained minimax and least squares problems in antenna array pattern synthesis","author":"J.C. Mason","year":"1987","unstructured":"J.C. Mason, S.J. Wilde and G. Opfer, Constrained minimax and least squares problems in antenna array pattern synthesis, Technical Note COMAG 1\/87, Royal Military College of Science, Computational Mathematics Group, Shrivenham, Swindon, Wiltshire, England (1987)."},{"key":"BF02139477_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-85643-3","volume-title":"Approximation of Functions: Theory and Numerical Methods","author":"G. Meinardus","year":"1967","unstructured":"G. Meinardus,Approximation of Functions: Theory and Numerical Methods (Springer, Berlin\/Heidelberg\/New York, 1967)."},{"key":"BF02139477_CR30","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/0021-9045(78)90082-5","volume":"23","author":"G. Opfer","year":"1978","unstructured":"G. Opfer, An algorithm for the construction of best approximations based on Kolmogorov's criterion, J. Approx. Theory 23 (1978) 299\u2013317.","journal-title":"J. Approx. Theory"},{"key":"BF02139477_CR31","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/BF01401045","volume":"32","author":"G. Opfer","year":"1979","unstructured":"G. Opfer, New extremal properties for constructing conformal mappings, Numer. Math. 32 (1979) 423\u2013429.","journal-title":"Numer. Math."},{"key":"BF02139477_CR32","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/BF01396315","volume":"35","author":"G. Opfer","year":"1980","unstructured":"G. Opfer, Conformal mappings onto prescribed regions via optimization techniques, Numer. Math. 35 (1980) 189\u2013200.","journal-title":"Numer. Math."},{"key":"BF02139477_CR33","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/BF01407872","volume":"39","author":"G. Opfer","year":"1982","unstructured":"G. Opfer, Solving complex approximation problems by semiinfinite-finite optimization techniques: a study on convergence, Numer. Math. 39 (1982) 411\u2013420.","journal-title":"Numer. Math."},{"key":"BF02139477_CR34","first-page":"T367","volume":"63","author":"G. Opfer","year":"1983","unstructured":"G. Opfer, Anwendung komplexer Approximation auf die L\u00f6sung linearer Gleichungssysteme mit der Richardson-Iteration, ZAMM 63 (1983) T367-T369.","journal-title":"ZAMM"},{"issue":"267","key":"BF02139477_CR35","first-page":"75","volume":"61","author":"G. Opfer","year":"1989","unstructured":"G. Opfer, Numerische Behandlung komplexer Approximationsaufgaben, Nova Acta Leopoldina NF 61, 267 (1989) 75\u201380.","journal-title":"Nova Acta Leopoldina NF"},{"key":"BF02139477_CR36","first-page":"201","volume":"3","author":"P.R. Owen","year":"1984","unstructured":"P.R. Owen and J.C. Mason, The use of linear programming in the design of antenna patterns with prescribed nulls and other constraints, Int. J. Comp. Math. in EEE 3 (1984) 201\u2013215.","journal-title":"Int. J. Comp. Math. in EEE"},{"key":"BF02139477_CR37","volume-title":"Digital Filter Design","author":"T.W. Parks","year":"1987","unstructured":"T.W. Parks and C.S. Burrus,Digital Filter Design (Wiley, New York, 1987)."},{"key":"BF02139477_CR38","unstructured":"A. Potchinkov and R. Reemtsen, The design of FIR filters in the complex domain by a semi-infinite programming technique, Preprint, Technische Universit\u00e4t Berlin (April 1992)."},{"key":"BF02139477_CR39","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/BF00940041","volume":"71","author":"R. Reemtsen","year":"1991","unstructured":"R. Reemtsen, Discretization methods for the solution of semi-infinite programming problems, J. Optim. Theory Appl. 71 (1991) 85\u2013103.","journal-title":"J. Optim. Theory Appl."},{"key":"BF02139477_CR40","unstructured":"R. Reemtsen, Outer approximation methods for semi-infinite optimization problems, Preprint No. 280\/1991, Fachbereich Mathematik, TU Berlin, 1000 Berlin 12 (1991)."},{"key":"BF02139477_CR41","volume-title":"Ein Abstiegsverfahren f\u00fcr Approximationsaufgaben in normierten R\u00e4umen","author":"R. Schultz","year":"1977","unstructured":"R. Schultz, Ein Abstiegsverfahren f\u00fcr Approximationsaufgaben in normierten R\u00e4umen, Ph.D. Thesis, Universit\u00e4t Hamburg, Hamburg (1977)."},{"key":"BF02139477_CR42","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1109\/JOE.1987.1145245","volume":"12","author":"M.S. Sherrill","year":"1987","unstructured":"M.S. Sherrill and R.L. Streit, In situ optimal reshading of arrays with failed elements, IEEE. J. Oceanic Eng. 12 (1987) 155\u2013162.","journal-title":"IEEE. J. Oceanic Eng."},{"key":"BF02139477_CR43","unstructured":"C. Spagl, Charakterisierung und Numerik in der linearen komplexen Tschebyscheff-Approximation, Ph.D. Thesis, Mathematisch-Geographische Fakult\u00e4t, Katholische Universit\u00e4t Eichst\u00e4tt (1988)."},{"key":"BF02139477_CR44","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1145\/214408.214415","volume":"11","author":"R.L. Streit","year":"1985","unstructured":"R.L. Streit, Algorithm 635. An algorithm for the solution of systems of complex linear equations in the L\u221e norm with constraints on the unknowns, ACM Trans. Math. Software 11 (1985) 242\u2013249.","journal-title":"ACM Trans. Math. Software"},{"key":"BF02139477_CR45","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/0024-3795(85)90266-6","volume":"64","author":"R.L. Streit","year":"1985","unstructured":"R.L. Streit, Saddle points and overdetermined complex equations, Lin. Alg. Appl. 64 (1985) 57\u201376.","journal-title":"Lin. Alg. Appl."},{"key":"BF02139477_CR46","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1137\/0907010","volume":"7","author":"R.L. Streit","year":"1986","unstructured":"R.L. Streit, Solution of systems of complex linear equations in the l\u221e norm with constraints on the unknowns, SIAM J. Sci. Stat. Comput. 7 (1986) 132\u2013149.","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"BF02139477_CR47","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1121\/1.388002","volume":"72","author":"R.L. Streit","year":"1982","unstructured":"R.L. Streit and A.H. Nuttall, A general Chebyshev complex function approximation procedure and an application to beamforming, J. Acoust. Soc. Amer. 72 (1982) 181\u2013190.","journal-title":"J. Acoust. Soc. Amer."},{"key":"BF02139477_CR48","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1090\/S0025-5718-1983-0689476-0","volume":"40","author":"R.L. Streit","year":"1983","unstructured":"R.L. Streit and A.H. Nuttall, A note on the semi-infinite programming approach to complex approximation, Math. Comp. 40 (1983) 599\u2013605.","journal-title":"Math. Comp."},{"key":"BF02139477_CR49","unstructured":"P.T.P. Tang, Chebyshev approximation on the complex plane, Ph.D. thesis, Department of Mathematics, University of California at Berkeley (May 1987)."},{"key":"BF02139477_CR50","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1090\/S0025-5718-1988-0935074-5","volume":"51","author":"P.T.P. Tang","year":"1988","unstructured":"P.T.P. Tang, A fast algorithm for linear complex Chebyshev approximations, Math. Comp. 51 (1988) 721\u2013739.","journal-title":"Math. Comp."},{"key":"BF02139477_CR51","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/978-1-4899-3442-0_24","volume-title":"Algorithms for Approximation II","author":"P.T.P. Tang","year":"1990","unstructured":"P.T.P. Tang, A fast algorithm for linear complex Chebyshev approximation, in:Algorithms for Approximation II, eds. J.C. Mason and M.G. Cox (Chapman and Hill, London\/New York, 1990) pp. 265\u2013273."},{"key":"BF02139477_CR52","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/0021-9045(81)90102-7","volume":"31","author":"L.N. Trefethen","year":"1981","unstructured":"L.N. Trefethen, Near circularity of the error curve in complex Chebyshev approximation, J. Approx. Theory 31 (1981) 344\u2013366.","journal-title":"J. Approx. Theory"},{"key":"BF02139477_CR53","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF01398258","volume":"37","author":"L.N. Trefethen","year":"1981","unstructured":"L.N. Trefethen, Rational Chebyshev approximation on the unit disk, Numer. Math. 37 (1981) 297\u2013320.","journal-title":"Numer. Math."},{"key":"BF02139477_CR54","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1093\/imanum\/8.4.461","volume":"8","author":"G.A. Watson","year":"1988","unstructured":"G.A. Watson, A method for the Chebyshev solution of an overdetermined system of complex linear equations, IMA J. Numer. Anal. 8 (1988) 461\u2013471.","journal-title":"IMA J. Numer. Anal."},{"key":"BF02139477_CR55","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1007\/978-1-4899-3442-0_23","volume-title":"Algorithms for approximation II","author":"G.A. Watson","year":"1990","unstructured":"G.A. Watson, Numerical methods for Chebyshev approximation of complex-valued functions, in:Algorithms for approximation II, eds. J.C. Mason and M.G. Cox (Chapman and Hill, London\/New York, 1990) pp. 246\u2013264."},{"key":"BF02139477_CR56","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1137\/0709053","volume":"9","author":"J. Williams","year":"1972","unstructured":"J. Williams, Numerical Chebyshev approximation in the complex plane, SIAM J. Numer. Anal. 9 (1972) 638\u2013649.","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02139477.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02139477\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02139477","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T11:46:05Z","timestamp":1557834365000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02139477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,10]]},"references-count":56,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1992,10]]}},"alternative-id":["BF02139477"],"URL":"https:\/\/doi.org\/10.1007\/bf02139477","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,10]]}}}