Most cited papers in Optimization and Variational Analysis
What are the most cited papers in Optimization and Variational Analysis?
The most cited paper in Optimization and Variational Analysis is "Optimal approximations by piecewise smooth functions and associated variational problems" (David B. Mumford, Jayant M. Shah, 1989), with 5,245 citations. Next come "A new approach to variable metric algorithms" (4,132) and "On Nonlinear Fractional Programming" (3,205).
Showing 50 of 100 papers. Every paper with more than 623 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Optimal approximations by piecewise smooth functions and associated variational problems David B. Mumford, Jayant M. Shah · Communications on Pure and Applied Mathematics | Jul 1989 | 5,245 |
| 2 | A new approach to variable metric algorithms Roger Fletcher · The Computer Journal | Mar 1970 | 4,132 |
| 3 | On Nonlinear Fractional Programming Werner Dinkelbach · Management Science | Mar 1967 | 3,205 |
| 4 | On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators Jonathan Eckstein, Dimitri P. Bertsekas · Mathematical Programming | Apr 1992 | 2,923 |
| 5 | On the stability of the linear mapping in Banach spaces Themistocles M. Rassias · Proceedings of the American Mathematical Society | Nov 1978 | 2,860 |
| 6 | The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming Lev M. Bregman · USSR Computational Mathematics and Mathematical Physics | 1967 | 2,699 |
| 7 | Set invariance in control Franco Blanchini · Automatica | Nov 1999 | 2,407 |
| 8 | Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems Garth P. McCormick · Mathematical Programming | Dec 1976 | 2,341 |
| 9 | Proximal Algorithms Neal Parikh, Stephen Boyd · Foundations and Trends® in Optimization | 2014 | 2,152 |
| 10 | A class of games possessing pure-strategy Nash equilibria Robert W. Rosenthal · International Journal of Game Theory | Dec 1973 | 2,060 |
| 11 | Minimization of functions having Lipschitz continuous first partial derivatives Larry Armijo · Pacific Journal of Mathematics | 1966 | 2,004 |
| 12 | Robust solutions of uncertain linear programs Aharon Ben‐Tal, Arkadi S. Nemirovski · Operations Research Letters | Aug 1999 | 1,855 |
| 13 | Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications Patrick T. Harker, Jong‐Shi Pang · Mathematical Programming | Mar 1990 | 1,828 |
| 14 | Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming A. L. Soyster · Operations Research | Oct 1973 | 1,812 |
| 15 | Proximal alternating linearized minimization for nonconvex and nonsmooth problems Jérôme Bolte, Shoham Sabach, Marc Teboulle · Mathematical Programming | 25 Jul 2013 | 1,776 |
| 16 | Restart procedures for the conjugate gradient method M. J. D. Powell · Mathematical Programming | Dec 1977 | 1,726 |
| 17 | On Projection Algorithms for Solving Convex Feasibility Problems Heinz H. Bauschke, Jonathan Michael Borwein · SIAM Review | Sep 1996 | 1,721 |
| 18 | Fuzzy differential equations Osmo Kaleva · Fuzzy Sets and Systems | Dec 1987 | 1,718 |
| 19 | Online convex programming and generalized infinitesimal gradient ascent Martin Zinkevich | 21 Aug 2003 | 1,691 |
| 20 | Iterative Algorithms for Nonlinear Operators Hong‐Kun Xu · Journal of the London Mathematical Society | Aug 2002 | 1,676 |
| 21 | A trust region method based on interior point techniques for nonlinear programming Richard H. Byrd, Jean Charles Gilbert, Jorge Nocedal · Mathematical Programming | Nov 2000 | 1,669 |
| 22 | Optimal control theory: An introduction W.S. Levine · IEEE Transactions on Automatic Control | Jun 1972 | 1,638 |
| 23 | Second-order cone programming Farid Alizadeh, Donald Goldfarb · Mathematical Programming | 2003 | 1,535 |
| 24 | A nonsmooth version of Newton's method Liqun Qi, Jie Sun · Mathematical Programming | 1993 | 1,495 |
| 25 | An outer-approximation algorithm for a class of mixed-integer nonlinear programs Marco A. Durán, Ignacio E. Grossmann · Mathematical Programming | Oct 1986 | 1,456 |
| 26 | An overview of bilevel optimization Benoît Colson, Patrice Marcotte, Gilles Savard · Annals of Operations Research | 20 Apr 2007 | 1,452 |
| 27 | Scenarios and Policy Aggregation in Optimization Under Uncertainty R. TYRRELL ROCKAFELLAR, Roger J.‐B. Wets · Mathematics of Operations Research | Feb 1991 | 1,357 |
| 28 | Integrals of set-valued functions Robert J. Aumann · Journal of Mathematical Analysis and Applications | Aug 1965 | 1,318 |
| 29 | Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources Hugh Everett · Operations Research | Jun 1963 | 1,275 |
| 30 | Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming R. TYRRELL ROCKAFELLAR · Mathematics of Operations Research | May 1976 | 1,226 |
| 31 | On sufficiency of the Kuhn-Tucker conditions Morgan A Hanson · Journal of Mathematical Analysis and Applications | Apr 1981 | 1,213 |
| 32 | Convex Approximations of Chance Constrained Programs Arkadi S. Nemirovski, Alexander Shapiro · SIAM Journal on Optimization | 22 Nov 2006 | 1,185 |
| 33 | Mirror descent and nonlinear projected subgradient methods for convex optimization Amir Beck, Marc Teboulle · Operations Research Letters | 25 Mar 2003 | 1,128 |
| 34 | Inequalities in Banach spaces with applications Hong‐Kun Xu · Nonlinear Analysis | 1991 | 1,095 |
| 35 | Nonmonotone Spectral Projected Gradient Methods on Convex Sets Ernesto G. Birgin, José Mario Martínez, Marcos Raydan · SIAM Journal on Optimization | 2000 | 1,093 |
| 36 | Engineering and Economic Applications of Complementarity Problems Michael C. Ferris, Jong‐Shi Pang · SIAM Review | 1997 | 1,082 |
| 37 | Global Convergence Properties of Conjugate Gradient Methods for Optimization Jean Charles Gilbert, Jorge Nocedal · SIAM Journal on Optimization | Feb 1992 | 1,072 |
| 38 | Iterative oblique projection onto convex sets and the split feasibility problem Charles L. Byrne · Inverse Problems | 7 Mar 2002 | 1,053 |
| 39 | Some NP-complete problems in quadratic and nonlinear programming Katta G. Murty, Santosh N. Kabadi · Mathematical Programming | Jun 1987 | 1,034 |
| 40 | Technical Note—A General Inner Approximation Algorithm for Nonconvex Mathematical Programs Barry Randall Marks, Gordon P. Wright · Operations Research | Aug 1978 | 1,034 |
| 41 | Disciplined Convex Programming Michael C. Grant, Stephen Boyd, Yinyu Ye · Kluwer Academic Publishers eBooks | 20 Jun 2006 | 1,030 |
| 42 | Construction of fixed points of nonlinear mappings in Hilbert space Felix E. Browder, W. V. Petryshyn · Journal of Mathematical Analysis and Applications | Nov 1967 | 1,030 |
| 43 | Submodular functions and convexity László Lovász | 1983 | 1,004 |
| 44 | A Survey of the Maximum Principles for Optimal Control Problems with State Constraints Richard F. Hartl, SURESH P. SETHI, Raymond G. Vickson · SIAM Review | Jun 1995 | 989 |
| 45 | Convergence of convex sets and of solutions of variational inequalities Umberto Mosco · Advances in Mathematics | Oct 1969 | 988 |
| 46 | Strongly Regular Generalized Equations Stephen M. Robinson · Mathematics of Operations Research | Feb 1980 | 988 |
| 47 | Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces Ky Fan · Proceedings of the National Academy of Sciences | Feb 1952 | 983 |
| 48 | NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE Felix E. Browder · Proceedings of the National Academy of Sciences | Oct 1965 | 966 |
| 49 | Function theory in polydiscs Walter Rudin · History of mathematics | Oct 1996 | 966 |
| 50 | Finite-time control of linear systems subject to parametric uncertainties and disturbances Francesco Amato, M. Ariola, P. Dorato · Automatica | Sep 2001 | 951 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.