Properties of Some Convex Marginal Functions Without Constant Rank Regularity

1999 ◽  
pp. 73-82 ◽  
Author(s):  
U. Würker
Keyword(s):  
Constant Rank ◽  
Marginal Functions

scholarly journals CONSTANT RANK CONSTRAINT QUALIFICATIONS: A GEOMETRIC INTRODUCTION

2014 ◽  
Vol 34 (3) ◽  
pp. 481-494 ◽  
Author(s):  
Roberto Andreani ◽  
Paulo J.S. Silva
Keyword(s):  
Constraint Qualifications ◽  
Constant Rank ◽  
Rank Constraint

A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition

2020 ◽  
Vol 37 (3) ◽  
pp. 1021-1047
Author(s):  
Roberto Andreani ◽  
Valeriano Antunes de Oliveira ◽  
Jamielli Tomaz Pereira ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Control Problems ◽  
Constant Rank ◽  
Rank Condition ◽  
Weak Maximum Principle

Abstract Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

Computation of subdifferentials of marginal functions using the distance function

Cybernetics ◽  
1990 ◽  
Vol 25 (5) ◽  
pp. 667-671 ◽  
Author(s):  
L. I. Minchenko
Keyword(s):  
Distance Function ◽  
Marginal Functions

Generalizations of Frobenius’ Theorem on Manifolds and Subcartesian Spaces

2007 ◽  
Vol 50 (3) ◽  
pp. 447-459 ◽  
Author(s):  
Jędrzej Śniatycki
Keyword(s):  
Vector Fields ◽  
Integral Manifold ◽  
Constant Rank ◽  
Frobenius Theorem

AbstractLet be a family of vector fields on a manifold or a subcartesian space spanning a distribution D. We prove that an orbit O of is an integral manifold of D if D is involutive on O and it has constant rank on O. This result implies Frobenius’ theorem, and its various generalizations, on manifolds as well as on subcartesian spaces.

Convex solutions of certain elliptic equations have constant rank hessians

1987 ◽  
Vol 97 (1) ◽  
pp. 19-32 ◽  
Author(s):  
Nicholas J. Korevaar ◽  
John L. Lewis
Keyword(s):  
Elliptic Equations ◽  
Constant Rank
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