Constant-Rank Condition and Second-Order Constraint Qualification

2010 ◽  
Vol 146 (2) ◽  
pp. 255-266 ◽  
Author(s):  
R. Andreani ◽  
C. E. Echagüe ◽  
M. L. Schuverdt
Keyword(s):  
Constraint Qualification ◽  
Second Order ◽  
Constant Rank ◽  
Rank Condition ◽  
Order Constraint

scholarly journals Notes on Constraint Qualifications for Second-Order Optimality Conditions

2019 ◽  
Vol 11 (5) ◽  
pp. 16
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualification ◽  
Constraint Qualifications ◽  
Second Order ◽  
Necessary Optimality Condition ◽  
First Order ◽  
Second Order Optimality Conditions ◽  
Order Constraint ◽  
Local Approximations ◽  
Abadie Constraint Qualification

In the first part of this paper we point out some basic properties of the critical cones used in second-order optimality conditions and give a simple proof of a strong second-order necessary optimality condition by assuming a “modified” first-order Abadie constraint qualification. In the second part we give some insights on second-order constraint qualifications related to second-order local approximations of the feasible set.

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.

scholarly journals On the necessity of the constant rank condition for L p estimates

2021 ◽  
Vol 358 (9-10) ◽  
pp. 1091-1095
Author(s):  
André Guerra ◽  
Bogdan Raiţă
Keyword(s):  
Constant Rank ◽  
Rank Condition

scholarly journals Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Shaohua Pan ◽  
Shujun Bi ◽  
Jein-Shan Chen
Keyword(s):  
Constraint Qualification ◽  
Optimal Solution ◽  
Second Order ◽  
Strong Regularity ◽  
Cone Programming ◽  
Second Order Cone Programming ◽  
Second Order Cone ◽  
Constraint Nondegeneracy ◽  
Robinson’S Constraint Qualification ◽  
Locally Optimal Solution

This paper is a counterpart of Bi et al., 2011. For a locally optimal solution to the nonlinear second-order cone programming (SOCP), specifically, under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB) nonsmooth system for the Karush-Kuhn-Tucker conditions, the strong second-order sufficient condition and constraint nondegeneracy, and the strong regularity of the Karush-Kuhn-Tucker point.

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