(1) The paper proposes a nonmonotonic BFGS - trust - region algorithm for unconstrained optimization.

(2) A nonmonotonic criterion is also used to speed up the convergence.

(3) In the third chapter, nonmonotonic trust region algorithms for nonlinear constrained optimization are discussed.

(4) Nonmonotonic reasoning systems including default logic logic are important in the commonsense reasoning of artificial intelligence.

(5) Nonmonotonic reasoning systems including default logic and autoepistemic logic are important in the commonsense reasoning of artificial intelligence.

(6) In the second chapter, nonmonotonic trust region algorithms for linear constrained optimization are discussed.

(7) Specifically, can chaotic behavior result in a single-loop feedback system with a nonmonotonic nonlinearity?

(8) The experiment with standard inductive reasoning tasks shows that the occurring of monotonic effect or nonmonotonic effect depends on the category relation between premises and the conclusion.

(9) This paper analyzes the characteristics and limitations of approximate reasoning (based on probability) and nonmonotonic reasoning (based on truth maintenance system).

(10) General logic programming is an important knowledge representation tool, and is an area of nonmonotonic reasoning.

(11) It can deal with the reasoning in an incomplete domain theory effectively and combine the advantages of approximate reasoning and nonmonotonic reasoning to overcome their limitations.