Generalized semi-infinite optimization: A first order optimality condition and examples

1998 ◽  
Vol 83 (1-3) ◽  
pp. 145-158 ◽  
Author(s):  
H. Th. Jongen ◽  
J. -J. Rückmann ◽  
O. Stein
Keyword(s):  
Optimality Condition ◽  
Order Optimality Condition ◽  
First Order

scholarly journals First-Order Necessary Conditions in Optimal Control

2021 ◽  
Author(s):  
David Mayne ◽  
Richard Vinter
Keyword(s):  
Optimal Control ◽  
Optimality Condition ◽  
State Constraints ◽  
Minimum Principle ◽  
Inequality Constraints ◽  
Problem Formulation ◽  
State Constraint ◽  
First Order ◽  
Accumulation Points ◽  
Minimax Condition

AbstractIn an earlier analysis of strong variation algorithms for optimal control problems with endpoint inequality constraints, Mayne and Polak provided conditions under which accumulation points satisfy a condition requiring a certain optimality function, used in the algorithms to generate search directions, to be nonnegative for all controls. The aim of this paper is to clarify the nature of this optimality condition, which we call the first-order minimax condition, and of a related integrated form of the condition, which, also, is implicit in past algorithm convergence analysis. We consider these conditions, separately, when a pathwise state constraint is, and is not, included in the problem formulation. When there are no pathwise state constraints, we show that the integrated first-order minimax condition is equivalent to the minimum principle and that the minimum principle (and equivalent integrated first-order minimax condition) is strictly stronger than the first-order minimax condition. For problems with state constraints, we establish that the integrated first-order minimax condition and the minimum principle are, once again, equivalent. But, in the state constrained context, it is no longer the case that the minimum principle is stronger than the first-order minimax condition, or vice versa. An example confirms the perhaps surprising fact that the first-order minimax condition is a distinct optimality condition that can provide information, for problems with state constraints, in some circumstances when the minimum principle fails to do so.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

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