Francis Clarke

Q: What Schools Are Affiliated With Francis Clarke

Francis Clarke is affiliated with the following schools: Université de Montréal, McGill University, University of British Columbia, Claude Bernard University Lyon 1, University of Washington

Francis Clarke 's AcademicInfluence.com Rankings

Francis Clarke

Mathematics

#3135

World Rank

#4689

Historical Rank

Measure Theory

#385

World Rank

#565

Historical Rank

mathematics Degrees

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Mathematics

Why Is Francis Clarke Influential?

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According to Wikipedia, Frank "Francis" H. Clarke is a Canadian and French mathematician. Biography Francis Clarke graduated in 1969 from McGill University with a B.Sc. degree in 1969 and in 1973 from the University of Washington with a Ph.D. with thesis advisor R. Tyrrell Rockafellar. In 1978 Clarke became a full professor at the University of British Columbia and gave an invited lecture at the International Congress of Mathematicians in Helsinki. In 1984 he was appointed director of the Centre de Recherches Mathématiques of the University of Montreal. During the nine years of his directorship, CRM became Canada's leading national research center for mathematics and its applications. The successes of Clarke's directorship included the creation of workshops and postdoctoral fellowships, thematic years, two series of publications, research awards, and an endowment fund. Francis Clarke is also the founding director of the Institut des Sciences Mathématiques of Quebec.

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Francis Clarke '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

Optimization And Nonsmooth Analysis (1983) (10177)
Nonsmooth analysis and control theory (1998) (2004)
Generalized gradients and applications (1975) (1116)
Functional Analysis, Calculus of Variations and Optimal Control (2013) (577)
Asymptotic controllability implies feedback stabilization (1997) (559)
The Optimal Exploitation of Renewable Resource Stocks: Problems of Irreversible Investment (1979) (474)
A New Approach to Lagrange Multipliers (1976) (466)
Proximal Smoothness and the Lower{C 2 Property (1995) (325)
On the inverse function theorem. (1976) (296)
Asymptotic Stability and Smooth Lyapunov Functions (1998) (266)
Methods of dynamic and nonsmooth optimization (1989) (254)
The Maximum Principle under Minimal Hypotheses (1976) (193)
Generalized gradients of Lipschitz functionals (1981) (169)
Regularity properties of solutions to the basic problem in the calculus of variations (1985) (168)
Hamiltonian trajectories having prescribed minimal period (1980) (167)
Shadow Prices and Duality for a Class of Optimal Control Problems (1979) (147)
Feedback Stabilization and Lyapunov Functions (2000) (147)
Nonlinear Analysis, Differential Equations and Control (1999) (144)
Nonlinear oscillations and boundary value problems for Hamiltonian systems (1982) (137)
Necessary Conditions In Dynamic Optimization (2005) (124)
Periodic solutions to Hamiltonian inclusions (1981) (119)
Optimal multiprocesses (1989) (119)
The relationship between the maximum principle and dynamic programming (1987) (113)
Necessary conditions for nonsmooth problems in-optimal control and the calculus of variations (1991) (103)
Nonsmooth optimization and related topics (1989) (95)
Mean value inequalities in Hilbert space (1994) (92)
Optimal Control Problems with Mixed Constraints (2010) (87)
Applications of optimal multiprocesses (1989) (84)
A classical variational principle for periodic Hamiltonian trajectories (1979) (66)
The Generalized Problem of Bolza (1976) (63)
Subgradient Criteria for Monotonicity, The Lipschitz Condition, and Convexity (1993) (61)
Optimal solutions to differential inclusions (1976) (61)
Monotone Invariant Solutions to Differential Inclusions (1977) (61)
Lyapunov Functions and Feedback in Nonlinear Control (2004) (54)
Local Optimality Conditions and Lipschitzian Solutions to the Hamilton–Jacobi Equation (1983) (51)
The Euler-Lagrange differential inclusion (1975) (47)
An indirect method in the calculus of variations (1993) (46)
COASTAL STATES, DISTANT WATER FISHING NATIONS AND EXTENDED JURISDICTION: A PRINCIPAL-AGENT ANALYSIS (1987) (45)
Proximal Analysis and Minimization Principles (1995) (44)
Nonsmooth Analysis in Control Theory: A Survey (2001) (43)
Lyapunov functions and discontinuous stabilizing feedback (2011) (43)
The value function in optimal control: Sensitivity, controllability, and time-optimality (1986) (42)
On the conditions under which the euler equation or the maximum principle hold (1984) (42)
On the Kummer congruences and the stable homotopy of U (1989) (41)
Existence and regularity in the small in the calculus of variations (1985) (39)
COASTAL STATES AND DISTANT WATER FISHING NATIONS: CONFLICTING VIEWS OF THE FUTURE (1991) (38)
Regularity properties of optimal controls (1990) (37)
Extremal arcs and extended Hamiltonian systems (1977) (36)
Admissible relaxation in variational and control problems (1975) (35)
Feedback in state constrained optimal control (2002) (35)
Continuity of solutions to a basic problem in the calculus of variations (2005) (35)
Necessary conditions, controllability and the value function for differential-difference inclusions (1986) (34)
GROSS'S LOGARITHMIC SOBOLEV INEQUALITY: A SIMPLE PROOF (1979) (33)
A Maximum Principle for Hybrid Optimal Control Problems with Pathwise State Constraints (2006) (32)
Partial subdifferentials, derivates and Rademacher’s Theorem (1999) (32)
A graph polynomial and its applications (1972) (32)
The universal von Staudt theorems (1989) (32)
OPTIMAL CONTROL AND THE TRUE HAMILTONIAN (1979) (31)
The Synthesis of Universal Feedback Pursuit Strategies in Differential Games (1997) (31)
Differential inclusions with free time (1988) (29)
Mean value inequalities (1994) (29)
Approximate Invariance and Differential Inclusions in Hilbert Spaces (1997) (27)
Perturbed optimal control problems (1986) (27)
Control of systems to sets and their interiors (1996) (27)
State Constrained Feedback Stabilization (2003) (26)
Pointwise Contraction Criteria for the Existence of Fixed Points (1978) (25)
A regularity theory for variational problems with higher order derivatives (1990) (24)
Complements, approximations, smoothings and invariance properties (1997) (24)
The value function in optimal control (1985) (24)
Necessary conditions for functional differential inclusions (1996) (24)
Sufficiency and the Jacobi Condition in the Calculus of Variations (1986) (23)
The nonsmooth maximum principle (2009) (23)
A proximal characterization of the reachable set (1996) (22)
Multiple integrals of Lipschitz functions in the calculus of variations (1977) (22)
Nonsmooth Analysis in Systems and Control Theory (2009) (22)
Dini Derivative and a Characterization for Lipschitz and Convex Functions on Riemannian Manifolds (2006) (21)
Fixed points and equilibria in nonconvex sets (1995) (20)
An intermediate existence theory in the calculus of variations (1989) (20)
The sensitivity of optimal control problems to time delay (1991) (19)
A decoupling principle in the calculus of variations (1993) (17)
Hamiltonian analysis of the generalized problem of Bolza (1987) (17)
Periodic solutions of Hamilton’s equations and local minima of the dual action (1985) (17)
The Erdmann Condition and Hamiltonian Inclusions in Optimal Control and the Calculus of Variations (1980) (17)
Stability analysis of sliding-mode feedback control (2009) (16)
Necessary Conditions for Nonsmooth Variational Problems (1974) (16)
Multicolorings, measures and games on graphs (1976) (16)
Maximum principles without differentiability (1975) (15)
The dual action, optimal control, and generalized gradients (1985) (15)
State constraints in optimal control: A case study in proximal normal analysis (1987) (15)
Invariance, monotonicity, and applications (1999) (14)
Approximate invariance and differential inclusions in Hilbert spaces (1997) (14)
On Global Optimality Conditions for Nonlinear Optimal Control Problems (1998) (14)
2. Generalized Gradients (1990) (14)
Optimal employment contracts in a principal-agent relationship (1983) (13)
The applicability of the Hamilton-Jacobi verification technique (1982) (12)
Inequality Constraints in the Calculus of Variations (1977) (12)
Asymptotic controllability implies control feedback stabilization (1997) (11)
Lyapunov and feedback characterizations of state constrained controllability and stabilization (2005) (11)
The Multidirectional Mean Value Theorem in Banach Spaces (1997) (11)
Optimal incentive schemes: Existence and characterization (1980) (11)
An Extension of the Schwarzkopf Multiplier Rule in Optimal Control (2011) (11)
The Hamilton-Jacobi Equation of Minimal Time Control (2004) (10)
On Hamiltonian Flows and Symplectic Transformations (1982) (10)
Journal of Convex Analysis (2012) (10)
A general theorem on necessary conditions in optimal control (2010) (10)
Nonconvex Duality in Optimal Control (2005) (9)
Geometric approximation on proximal normals. (1997) (9)
Hamilton-Jacobi characterization of the state constrained value (2005) (8)
New skeletal-space-filling models. A model of an enzyme active site. (1977) (8)
The Proximal Subgradient and Constancy (1993) (8)
Universal Feedback Control via Proximal Aiming in Problems of Control under Disturbance and Differential Games (1999) (6)
Variational Problems with Lipschitzian Minimizers (1989) (6)
Asymptotic Controllability And Feedback Stabilization (1996) (6)
Calculator Programming for Chemistry and the Life Sciences (1981) (6)
The Integrality of the Values of Bernoulli Polynomials and of Generalised Bernoulli Numbers (1997) (5)
A variational proof of Aumann's theorem (1981) (5)
The Calculus of Variations, Nonsmooth Analysis and Optimal Control (2000) (5)
Tonelli's regurarity theory in the calculus of variations: Recent progress (1986) (5)
On Connections Between the Maximum Principle and the Dynamic Programming Technique (1986) (3)
Global optimality in the calculus of variations (1997) (3)
Intermediate existence and regularity in the calculus of variations (1988) (3)
Regularity properties of solutions to linear quadratic optimal control problems with state constraints (1997) (3)
SUFFICIENT CONDITIONS FOR THE GENERALIZED PROBLEM OF BOLZA (2009) (3)
Geometric Control and Nonsmooth Analysis (2006) (3)
Solving equations by the decrease principle (1997) (3)
Optimal Pricing in the Presence of Experience Effects (1982) (3)
Shadow Prices, Duality and Green's Formula for a Class of Optimal Control Problems. (1978) (2)
Sensitivity analysis in optimal control (1984) (2)
Review: Lucien W. Neustadt, Optimization, a theory of necessary conditions, and W. G. Boltjanski, Optimale Steuerung diskreter Systeme, and R. Gabasov and F. Kirillova, The qualitative theory of optimal processes (1978) (2)
Necessary conditions in optimal control: a new approach (2003) (2)
On the Homology of Sp (1981) (1)
The Optimal Exploitation of Renewable Resource Stocks: Problems of Irreversible Investment 1 (2019) (1)
APPLICATIONS OF PROXIMAL SUBGRADIENTS (1989) (1)
Addendum to “regularity properties of solutions to linear quadratic optimal control problems with state constraints” [systems control lett. 30 (1997) 265–272] (1998) (1)
Geometric Control And Nonsmooth Analysis: In Honor of the 73rd Birthday of H Hermes and of the 71st Birthday of R T Rockafellar (2008) (1)
1. Introduction and Preview (1990) (1)
4. Optimal Control (1989) (1)
Inner Approximation of State-Constrained Optimal Control Problems (2001) (1)
Proximal techniques of feedback construction (1998) (1)
6. Mathematical Programming (1990) (0)
STABILITY ANALYSIS OF SLIDING MODE CONTOLLERS (2008) (0)
CHAPTER 3 – Potentiometric Titrations (1981) (0)
4. The Calculus of Variations (1990) (0)
The Necessary Conditions for Optimal Control in Hilbert Spaces (2003) (0)
EXTREMAL ARCS AND EXTENDED HAMILTONIAN SYSTEMS * 1 ) (2010) (0)
Bases for Caribbean integration: Caribbean non-governmental organizations and Caribbean integration (2008) (0)
CHAPTER 1 – Molecular Formulas (1981) (0)
New Skeletal-Space-Filling Models. (1977) (0)
1. Nonsmooth Analysis and Geometry (1989) (0)
Continued Fraction Expansions and the Legendre Polynomials (1986) (0)
Regularity of solutions to one-dimensional and multi-dimensional problems in the calculus of variations (2008) (0)
Control and Cybernetics the Nonsmooth Maximum Principle * (2010) (0)
2. The Basic Problem in the Calculus of Variations (1989) (0)
7. Topics in Analysis (1990) (0)
Controllability and sensitivity of control problems with respect to time delay (1991) (0)
CHAPTER 4 – Correlation Analysis (1981) (0)
Ju l 2 00 7 Regularity of solutions to higher-order integrals of the calculus of variations (2018) (0)
OPTIMIZATION AND PERIODIC TRAJECTORIES (1987) (0)
5. Optimal Control (1990) (0)
3. Differential Inclusions (1990) (0)
Book Review: The qualitative theory of optimal processes (1978) (0)
3. Verification Functions and Dynamic Programming (1989) (0)
Existence of solutions in dynamic optimization (1991) (0)
CHAPTER 2 – Coordinate Transformations (1981) (0)

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What Schools Are Affiliated With Francis Clarke ?

Francis Clarke is affiliated with the following schools: