Quasi-Convex Programming

Previous article Next article Quasi-Convex ProgrammingDavid G. LuenbergerDavid G. Luenbergerhttps://doi.org/10.1137/0116088PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] O. L. Mangasarian, Pseudo-convex functions, J. Soc. Indust. Appl. Math. Ser. A Control, 3 (1965), 281–290 MR0191659 (32:9062) 0138.15702 LinkGoogle Scholar[2] J. Rissanen, On duality without convexity, J. Math. Anal. Appl., 18 (1967), 269–275 10.1016/0022-247X(67)90057-1 MR0213160 (35:4025) 0183.22701 CrossrefISIGoogle Scholar[3] Kenneth J. Arrow and , Alain C. Enthoven, Quasi-concave programming, Econometrica, 29 (1961), 779–800 MR0138509 (25:1956) 0104.14302 CrossrefISIGoogle Scholar[4] M. Slater, Lagrange multipliers revisited: a contribution to nonlinear programming, Cowles Commission Discussion Paper, Math. 403, 1950 Google Scholar[5] W. Fenchel, Convex cones, sets, and functions, Lecture notes, Department of Mathematics, Princeton University, Princeton, 1953 0053.12203 Google Scholar[6] Samuel Karlin, Mathematical methods and theory in games, programming and economics. Vol. I: Matrix games, programming, and mathematical economics. Vol. II: The theory of infinite games, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1959Vol. I, x+433 pp. Vol. II, xi+386 MR0111634 (22:2496) Google Scholar[7] Maurice Sion, On general minimax theorems, Pacific J. Math., 8 (1958), 171–176 MR0097026 (20:3506) 0163.38203 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Revenue-Maximizing Resource Allocation for Multitenant Cell-Free Massive MIMO NetworksIEEE Systems Journal, Vol. 16, No. 2 Cross Ref Duality for quasiconvex minimization over closed convex cones11 June 2021 | Optimization Letters, Vol. 15 Cross Ref Disciplined quasiconvex programming2 March 2020 | Optimization Letters, Vol. 14, No. 7 Cross Ref Some Remarks on Greenberg–Pierskalla Subdifferentiability of Quasiconvex Functions6 March 2020 | Vietnam Journal of Mathematics, Vol. 48, No. 2 Cross Ref Duality Theorems for Convex and Quasiconvex Set Functions21 February 2020 | SN Operations Research Forum, Vol. 1, No. 1 Cross Ref Multi-User Downlink Communication28 November 2019 Cross Ref Evenly Convex Functions28 October 2020 Cross Ref Indefinite multi-constrained separable quadratic optimization: Large-scale efficient solutionEuropean Journal of Operational Research, Vol. 278, No. 1 Cross Ref Inequality-minimization with a given public budget27 April 2018 | The Journal of Economic Inequality, Vol. 16, No. 4 Cross Ref On the Design of an Intelligent Speed Advisory System for Cyclists Cross Ref Multi-Armed Bandit Learning in IoT Networks: Learning Helps Even in Non-stationary Settings17 February 2018 Cross Ref Generalising quasi-LPV and CDI models to Quasi-Convex Difference InclusionsIFAC-PapersOnLine, Vol. 50, No. 1 Cross Ref Cramér's Theorem is Atypical20 August 2016 Cross Ref Continuity of Optimal Solution Functions and their Conditions on Objective FunctionsYasushi Terazono and Ayumu Matani20 October 2015 | SIAM Journal on Optimization, Vol. 25, No. 4AbstractPDF (221 KB)ON SURROGATE DUALITY FOR ROBUST SEMI-INFINITE OPTIMIZATION PROBLEMJournal of the Chungcheong Mathematical Society, Vol. 27, No. 3 Cross Ref Near-Field Passive RFID Communication: Channel Model and Code DesignIEEE Transactions on Communications, Vol. 62, No. 5 Cross Ref Zero duality gap in surrogate constraint optimization: A concise review of modelsEuropean Journal of Operational Research, Vol. 232, No. 2 Cross Ref Strong and Total Lagrange Dualities for Quasiconvex ProgrammingJournal of Applied Mathematics, Vol. 2014 Cross Ref Surrogate duality for robust optimizationEuropean Journal of Operational Research, Vol. 231, No. 2 Cross Ref On the Duality of the Max–Min Beamforming Problem With Per-Antenna and Per-Antenna-Array Power ConstraintsIEEE Transactions on Vehicular Technology, Vol. 62, No. 2 Cross Ref A complete characterization of strong duality in nonconvex optimization with a single constraint18 February 2011 | Journal of Global Optimization, Vol. 53, No. 2 Cross Ref Necessary and Sufficient Constraint Qualification for Surrogate Duality9 August 2011 | Journal of Optimization Theory and Applications, Vol. 152, No. 2 Cross Ref An effective immune based two-phase approach for the optimal reliability–redundancy allocation problemApplied Mathematics and Computation, Vol. 218, No. 4 Cross Ref Under-Determined Non-cartesian MR Reconstruction with Non-convex Sparsity Promoting Analysis Prior Cross Ref Solving the Redundancy Allocation Problem With a Mix of Components Using the Improved Surrogate Constraint MethodIEEE Transactions on Reliability, Vol. 56, No. 1 Cross Ref Bibliography Cross Ref A method for determining optimal multipliers in the surrogate constraint method1 January 2005 | Electronics and Communications in Japan (Part III: Fundamental Electronic Science), Vol. 88, No. 8 Cross Ref Surrogate Programming and Multipliers in Quasi-convex ProgrammingJean-Paul Penot and Michel Volle26 July 2006 | SIAM Journal on Control and Optimization, Vol. 42, No. 6AbstractPDF (143 KB)System Reliability Optimization: An Overview Cross Ref Convex Sets. 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