Olvi L. Mangasarian | Academic Influence

Olvi L. Mangasarian's AcademicInfluence.com Rankings

Olvi L. Mangasarian

Mathematics

#3342

World Rank

#4952

Historical Rank

#1252

USA Rank

Measure Theory

#290

World Rank

#450

Historical Rank

#128

USA Rank

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Mathematics

Olvi L. Mangasarian's Degrees

PhD Mathematics University of California, Berkeley
Masters Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Olvi L. Mangasarian Influential?

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According to Wikipedia, Olvi Leon Mangasarian was the John von Neumann Professor Emeritus of Mathematics and Computer Sciences in Department of Mathematics, University of California, San Diego and Professor Emeritus of Computer Sciences at the University of Wisconsin-Madison and a recognised expert on optimization, data mining, and classification. In 2000, while professor in the Computer Science Department of the University of Wisconsin–Madison, he was awarded the Frederick W. Lanchester Prize for pioneering work in introducing the use of Operations Research techniques to the field of data mining with a particularly notable application being to breast cancer diagnosis.

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Olvi L. Mangasarian's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Nonlinear Programming (1969) (1863)
Feature Selection via Concave Minimization and Support Vector Machines (1998) (1115)
Multisurface method of pattern separation for medical diagnosis applied to breast cytology. (1990) (1060)
Proximal support vector machine classifiers (2001) (896)
Breast Cancer Diagnosis and Prognosis Via Linear Programming (1995) (856)
Robust linear programming discrimination of two linearly inseparable sets (1992) (833)
RSVM: Reduced Support Vector Machines (2001) (727)
Multisurface proximal support vector machine classification via generalized eigenvalues (2006) (669)
The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints (1967) (642)
SSVM: A Smooth Support Vector Machine for Classification (2001) (585)
Lagrangian Support Vector Machines (2001) (579)
Nuclear feature extraction for breast tumor diagnosis (1993) (547)
A class of smoothing functions for nonlinear and mixed complementarity problems (1996) (506)
Successive overrelaxation for support vector machines (1999) (453)
Linear and Nonlinear Separation of Patterns by Linear Programming (1965) (361)
Multicategory Proximal Support Vector Machine Classifiers (2005) (337)
Sufficient Conditions for the Optimal Control of Nonlinear Systems (1966) (327)
Pattern Recognition Via Linear Programming: Theory and Application to Medical Diagnosis (1989) (322)
A Feature Selection Newton Method for Support Vector Machine Classification (2004) (314)
Solution of symmetric linear complementarity problems by iterative methods (1977) (302)
Clustering via Concave Minimization (1996) (298)
Smoothing methods for convex inequalities and linear complementarity problems (1995) (294)
Mathematical Programming for Data Mining: Formulations and Challenges (1999) (283)
Absolute value equations (2006) (267)
Second- and higher-order duality in nonlinear programming☆ (1975) (261)
PSEUDO-CONVEX FUNCTIONS (1965) (253)
A generalized Newton method for absolute value equations (2009) (227)
Semi-superyised support vector machines for unlabeled data classification (2001) (225)
Feature Selection via Mathematical Programming (1997) (223)
Nonlinear complementarity as unconstrained and constrained minimization (1993) (214)
Exact penalty functions in nonlinear programming (1979) (214)
Generalized Support Vector Machines (1998) (210)
Machine learning techniques to diagnose breast cancer from image-processed nuclear features of fine needle aspirates. (1994) (209)
Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems (1987) (208)
Equivalence of the Complementarity Problem to a System of Nonlinear Equations (1976) (203)
Knowledge-Based Support Vector Machine Classifiers (2002) (200)
Arbitrary-norm separating plane (1999) (196)
Massive data discrimination via linear support vector machines (2000) (194)
Absolute value programming (2007) (194)
A finite newton method for classification (2002) (181)
Multicategory discrimination via linear programming (1994) (178)
NONLINEAR PERTURBATION OF LINEAR PROGRAMS (1979) (178)
On Concepts of Directional Differentiability (2004) (177)
A simple characterization of solution sets of convex programs (1988) (175)
Robust Linear and Support Vector Regression (2000) (173)
Two-person nonzero-sum games and quadratic programming (1964) (164)
Incremental Support Vector Machine Classification (2002) (164)
Absolute value equation solution via concave minimization (2006) (157)
Image analysis and machine learning applied to breast cancer diagnosis and prognosis. (1995) (151)
Computer-derived nuclear features distinguish malignant from benign breast cytology. (1995) (149)
Exact 1-Norm Support Vector Machines Via Unconstrained Convex Differentiable Minimization (2006) (141)
Mathematical Programming in Neural Networks (1993) (133)
Mathematical Programming in Data Mining (1997) (132)
Multisurface method of pattern separation (1968) (131)
Bilinear separation of two sets inn-space (1993) (130)
Serial and parallel backpropagation convergence via nonmonotone perturbed minimization (1994) (118)
Linear complementarity problems solvable by A single linear program (1976) (118)
Finite Newton method for Lagrangian support vector machine classification (2003) (114)
Superlinearly convergent quasi-newton algorithms for nonlinearly constrained optimization problems (1976) (113)
Parallel Variable Distribution (1994) (108)
Machine Learning via Polyhedral Concave Minimization (1996) (106)
Uniqueness of solution in linear programming (1979) (106)
Knowledge-Based Kernel Approximation (2004) (105)
Multiple Instance Classification via Successive Linear Programming (2008) (103)
Active Support Vector Machine Classification (2000) (96)
Parallel Gradient Distribution in Unconstrained Optimization (1995) (94)
Duality in nonlinear programming (1962) (92)
Large Scale Kernel Regression via Linear Programming (2002) (88)
New improved error bounds for the linear complementarity problem (1994) (88)
Data selection for support vector machine classifiers (2000) (87)
Financial Asset-Pricing Theory and Stochastic Programming Models for Asset/ Liability Management: a Synthesis (1996) (84)
A Condition Number for Differentiable Convex Inequalities (1985) (84)
Importance of nuclear morphology in breast cancer prognosis. (1999) (84)
A Newton Method for Linear Programming (2004) (83)
Unconstrained Lagrangians in Nonlinear Programming (1975) (82)
Characterization of linear complementarity problems as linear programs (1978) (81)
Misclassification minimization (1994) (79)
Equilibrium Points of Bimatrix Games (1964) (79)
New Error Bounds for the Linear Complementarity Problem (1994) (78)
DISCRETE SPLINES VIA MATHEMATICAL PROGRAMMING. (1971) (77)
Nonlinear Knowledge in Kernel Approximation (2007) (76)
Normal solutions of linear programs (1984) (76)
Privacy-preserving classification of vertically partitioned data via random kernels (2008) (76)
Probability of unique integer solution to a system of linear equations (2011) (75)
Computerized breast cancer diagnosis and prognosis from fine-needle aspirates. (1995) (75)
Breast cytology diagnosis with digital image analysis. (1993) (71)
Error bounds for monotone linear complementarity problems (1986) (71)
An Inductive Learning Approach to Prognostic Prediction (1995) (70)
Sparse Kernel Feature Analysis (2002) (70)
Linear and Convex Programming (1966) (70)
Iterative Solution of Linear Programs (1981) (69)
Complementarity: Applications, Algorithms and Extensions (2010) (68)
Locally unique solutions of quadratic programs, linear and nonlinear complementarity problems (1980) (67)
Knowledge-Based Nonlinear Kernel Classifiers (2003) (66)
Breast cancer survival and chemotherapy: A support vector machine analysis (1999) (65)
Linear programming with MATLAB (2007) (65)
Sufficiency of exact penalty minimization (1985) (64)
Set Containment Characterization (2002) (64)
Survival-Time Classification of Breast Cancer Patients (2003) (63)
Nonlinear Knowledge-Based Classification (2008) (63)
Characterizations of Real Matrices of Monotone Kind (1968) (63)
Feature Selection for Nonlinear Kernel Support Vector Machines (2007) (63)
Minimal Kernel Classifiers (2003) (62)
Privacy-preserving horizontally partitioned linear programs (2012) (61)
Feeling Stressed and Burned Out: a Feminist Reading and Re-Visioning of Stress-Based Emotions Within Medicine and Organization Science (1998) (61)
The linear complementarity problem as a separable bilinear program (1995) (58)
Minimum-support solutions of polyhedral concave programs * (1999) (57)
Equivalence of Minimal ℓ0- and ℓp-Norm Solutions of Linear Equalities, Inequalities and Linear Programs for Sufficiently Small p (2011) (56)
Inequalities for Stochastic Nonlinear Programming Problems (1964) (56)
Privacy-Preserving Classification of Horizontally Partitioned Data via Random Kernels (2008) (55)
Error bounds for nondegenerate monotone linear complementarity problems (1990) (54)
Sparsity-preserving sor algorithms for separable quadratic and linear programming (1984) (54)
The Extended Linear Complementarity Problem (1995) (53)
Plastic Stress Concentration at a Circular Hole in an Infinite Sheet Subjected to Equal Biaxial Tension (1960) (51)
Knapsack feasibility as an absolute value equation solvable by successive linear programming (2009) (49)
Data Discrimination via Nonlinear Generalized Support Vector Machines (2001) (47)
Best Summation Formulae and Discrete Splines (1973) (46)
Convergence of Iterates of an Inexact Matrix Splitting Algorithm for the Symmetric Monotone Linear Complementarity Problem (1991) (46)
Hybrid misclassification minimization (1996) (46)
Minimum principle sufficiency (1992) (43)
A dual differentiable exact penalty function (1983) (40)
A variable-complexity norm maximization problem (1986) (40)
Absolute value equation solution via dual complementarity (2013) (40)
Parsimonious Least Norm Approximation (1998) (39)
Data Mining via Support Vector Machines (2001) (37)
Minmax and duality in nonlinear programming (1965) (37)
Privacy-preserving linear programming (2011) (37)
CONVEXITY, PSEUDO-CONVEXITY AND QUASI-CONVEXITY OF COMPOSITE FUNCTIONS (1975) (35)
Linear complementarity as absolute value equation solution (2014) (35)
Asynchronous parallel successive overrelaxation for the symmetric linear complementarity problem (1988) (34)
A hybrid algorithm for solving the absolute value equation (2015) (34)
Perron-Frobenius properties of Ax − λBx (1971) (33)
Primal-dual bilinear programming solution of the absolute value equation (2012) (33)
Parallel gradient projection successive overrelaxation for symmetric linear complementarity problems and linear programs (1988) (32)
Backpropagation Convergence via Deterministic Nonmonotone Perturbed Minimization (1993) (32)
Computer-derived nuclear "grade" and breast cancer prognosis. (1995) (32)
Finite perturbation of convex programs (1991) (31)
Absolute Value Equation Solution Via Linear Programming (2014) (31)
Simplified Characterizations of Linear Complementarity Problems Solvable as Linear Programs (1979) (30)
Serial and Parallel Solution of Large Scale Linear Programs by Augmented Lagrangian Successive Overrelaxation (1988) (30)
Nonlinear Programming Problems with Stochastic Objective Functions (1964) (28)
Parallel Constraint Distribution (1991) (27)
Error bounds for nondifferentiable convex inequalities under a strong Slater constraint qualification (1998) (26)
Computer-aided diagnosis of breast aspirates via expert systems. (1990) (26)
Support vector machine classification via parameterless robust linear programming (2005) (25)
Knowledge-Based Linear Programming (2005) (25)
Simple bounds for solutions of monotone complementarity problems and convex programs (1985) (25)
A Condition Number for Linear Inequalities and Linear Programs. (1981) (25)
Solution of linear complementarity problems by linear programming (1976) (24)
Indeterminate fine‐needle aspiration of the breast (1997) (23)
A Stable Theorem of the Alternative: An Extension of the Gordan Theorem. (1981) (23)
A Finite Newton Method for Classi cation Problems (2001) (23)
Simple computable bounds for solutions of linear complementarity problems and linear programs (1985) (22)
Logarithmic convexity and geometric programming (1968) (22)
Characterizations of bounded solutions of linear complementarity problems (1982) (21)
A Linearly Convergent Derivative-Free Descent Method for Strongly Monotone Complementarity Problems (1999) (21)
Exact Penalty Functions for Mathematical Programs with Linear Complementarity Constraints (1996) (21)
Linear Programming with MATLAB (MPS-SIAM Series on Optimization) (2008) (21)
Optimization methods in massive data sets (2002) (21)
Global Minimization via Piecewise-Linear Underestimation (2005) (20)
Optimality Conditions in Smooth Nonlinear Programming (18)
Error bounds and strong upper semicontinuity for monotone affine variational inequalities (1993) (18)
Conjugate Cone Characterization of Positive Definite and Semidefinite Matrices. (1984) (18)
Improved Generalization via Tolerant Training (1998) (18)
Local Duality of Nonlinear Programs (1984) (17)
Least-norm linear programming solution as an unconstrained minimization problem☆ (1983) (17)
Complementarity: Applications, Algorithms and Extensions (Applied Optimization) (2001) (16)
Mathematical programming approaches to machine learning and data mining (1998) (15)
Computational optimization : a tribute to Olvi Mangasarian (1999) (15)
Feature Selection in k-Median Clustering (2004) (15)
Computer-designed expert systems for breast cytology diagnosis. (1993) (15)
Massive Support Vector Regression (1999) (14)
Some Applications of Penalty Functions in Mathematical Programming. (1986) (14)
Exact penalty for mathematical programs with linear complementarity constraints (1997) (14)
Serial and Parallel Multicategory Discrimination (1994) (14)
Stability Criteria for Nonlinear Ordinary Differential Equations (1963) (14)
Mathematical Programming in Machine Learning (1996) (14)
Support vector machines in data mining (2001) (13)
Computable numerical bounds for lagrange multipliers of stationary points of non-convex differentiable non-linear programs (1985) (13)
A convergent splitting of matrices (1970) (13)
Multi-sweep asynchronous parallel successive overrelaxation for the nonsymmetric linear complementarity problem (1990) (13)
Numerical solution of the first biharmonic problem by linear programming (1963) (12)
Unsupervised classification via convex absolute value inequalities (2015) (12)
Breast Cytology Diagnosis via Digital Image Analysis 1 2 3 (1993) (12)
Nonconvex Piecewise-Quadratic Underestimation for Global Minimization (2006) (12)
Global error bounds for monotone affine variational inequality problems (1992) (11)
Privacy-Preserving Random Kernel Classification of Checkerboard Partitioned Data (2010) (11)
The Ill-Posed Linear Complementarity Problem (1995) (11)
Polyhedral Boundary Projection (1999) (11)
Privacy-preserving linear and nonlinear approximation via linear programming (2013) (10)
Regularized Linear Programs with Equilibrium Constraints (1998) (8)
Machine learning and data mining via mathematical programming-based support vector machines (2003) (8)
Sufficient conditions for the unsolvability and solvability of the absolute value equation (2017) (8)
Breast Tumor Susceptibility to Chemotherapy Via Support Vector Machines (2006) (7)
Nonlinear knowledge in kernel machines (2008) (7)
Uniqueness of integer solution of linear equations (2010) (7)
An Interior-Point Method for Multifractional Programs with Convex Constraints (6)
Error bounds for inconsistent linear inequalities and programs (1994) (6)
Proximal Knowledge‐based Classification (2009) (6)
Equivalence in nonlinear programming (1963) (6)
Hybrid Misclassi cation Minimization (1995) (6)
Characterization of Positive Definite and Semidefinite Matrices via Quadratic Programming Duality. (1982) (6)
A conjugate decomposition of the Euclidean space. (1983) (5)
Chunking for massive nonlinear kernel classification (2008) (5)
7. Optimality Criteria in Nonlinear Programming with Differentiability (1994) (5)
Solution of the linear inverse vector optimization problem by a single linear program (1978) (4)
Individual and Collective Prognostic Prediction (1996) (4)
Convex Kernel Underestimation of Functions with Multiple Local Minima (2006) (4)
Optimization-based machine learning and data mining (2008) (2)
Optimal simplex tableau characterization of unique and bounded solutions of linear programs (1981) (2)
Unsupervised and Semisupervised Classification Via Absolute Value Inequalities (2016) (2)
Clustering via Concave MinimizationP (2)
2. Linear Inequalities and Theorems of the Alternative (1994) (2)
Proximal Knowledge-based Classification (2009) (2)
Parsimonious side propagation (1998) (2)
Nonlinear programming, 2 : proceedings of the Special Interest Group on Mathematical Programming Symposium, conducted by the Computer Sciences Department at the University of Wisconsin--Madison, April 15-17, 1974 (1975) (2)
Privacy-preserving horizontally partitioned linear programs (2010) (1)
Data Mining via Generalized Support Vector Machines (2003) (1)
1. The Nonlinear Programming Problem, Preliminary Concepts, and Notation (1994) (1)
Iterative solution of linear programs. [By solving quadratic program in its dual variable space] (1979) (1)
Correction to the paper “Duality in nonlinear programming” (1963) (1)
Nonlinear programming 3 : proceedings of the Special Interest Group on Mathematical Programming symposium (1978) (1)
9. Generalizations of Convex Functions: Quasiconvex, Strictly Quasiconvex, and Pseudoconvex Functions (1994) (1)
Finite Convergence of Algorithms for Nonlinear (1)
Book Review:Selected Applications of Nonlinear Programming. Jerome Bracken, Garth P. McCormick (1969) (1)
OPTIMALITY AND DUALITY IN NONLINEAR PROGRAMMING (2015) (1)
Quadratic Convergence of a Newton Method for Nonlinear Programming (1972) (1)
Center for Parallel Optimization. (1996) (0)
2 Equivalence of Primal Exterior Penalty LP to Dual Least 2-Norm LP (0)
11. Optimality and Duality in the Presence of Nonlinear Equality Constraints (1994) (0)
8. Interior-Point Methods (2007) (0)
Nonlinear programming 4 : proceedings of the Nonlinear Programming Symposium 4 (1981) (0)
Sufficient conditions for the unsolvability and solvability of the absolute value equation (2017) (0)
Primal-dual bilinear programming solution of the absolute value equation (2011) (0)
Asymptotic Properties of the Fenchel Dual Functional and Applications to Decomposition Problems (0)
Absolute Value Equation Solution Via Linear Programming (2013) (0)
6. Sensitivity and Parametric Linear Programming (2007) (0)
7. Quadratic Programming and Complementarity Problems (2007) (0)
SSVM: A Amooth Support Vector Machine for Classification (1999) (0)
Monotone Splitting of matrices (1974) (0)
10. Optimality and Duality for Generalized Convex and Concave Functions (1994) (0)
Linear complementarity as absolute value equation solution (2013) (0)
5. Solving Large Linear Programs (2007) (0)
Notes on a Panel Discussion on Benchmarks at INFORMS Puerto Rico , July 2007 (2008) (0)
First-Order Conditions for Isolated Locally Optimal Solutions 1 (1993) (0)
Absolute value equation solution via dual complementarity (2012) (0)
Primal - Dual Parallel Solution of Very Large Sparse Linear Programs. (1987) (0)
Unsupervised and Semisupervised Classification Via Absolute Value Inequalities (2015) (0)
Wolberg 1 Image Analysis and Machine Learning Applied to Breast Cancer Diagnosis and Prognosis (2009) (0)
6. Differentiable Convex and Concave Functions (1994) (0)
9. Approximation and Classification (2007) (0)
A hybrid algorithm for solving the absolute value equation (2015) (0)
Dedication (1996) (0)
5. Saddlepoint Optimality Criteria of Nonlinear Programming without Differentiability (1994) (0)
8. Duality in Nonlinear Programming (1994) (0)
4. Convex and Concave Functions (1994) (0)
PSEUDO-CONVEX FUNCTIONS* (1975) (0)
Parallel Solution of Very Large Sparse Linear Programs (1990) (0)
Convergent Generalized Monotone Splitting of Matrices (1971) (0)
Sparse Kernel Feature (1999) (0)
A Class of Smoothing Functionsfor Nonlinear and Mixed Complementarity ProblemsDedicated to (2013) (0)
3. The Simplex Method (2007) (0)
Dedication: Richard Warren Cottle (1996) (0)
3. Convex Sets in Rn (1994) (0)
2. Linear Algebra: A Constructive Approach (2007) (0)

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