An Alternative Regularity Condition for Hajek's Representation Theorem

An Alternative Representation for QBF

Quantified Boolean formulas are a powerful representation that have been used to capture and solve a variety of problems in Artificial Intelligence. While most research has focused on quantified Boolean formulas in prenex normal form (QBF), we explore an alternative representation of quantified Boolean formulas, called Constrained Quantified Formulas (CQF). CQF allows for a more direct represen...

An Induction Theorem and Nonlinear Regularity

A general nonlinear regularity model for a set-valued mapping F : X × R+ ⇒ Y , where X and Y are metric spaces, is studied using special iteration procedures, going back to Banach, Schauder, Lyusternik and Graves. Namely, we revise the induction theorem from Khanh, J. Math. Anal. Appl., 118 (1986) and employ it to obtain basic estimates for exploring regularity/openness properties. We also show...

A utility representation theorem with weaker continuity condition

We prove that a preference relation which is continuous on every straight line has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but our condition on the continuity of a preference relation is strictly weaker than theirs. JEL classific...

Extension on Regularity Condition in DEA Models

AppGP: An alternative structural representation for GP

It has been shown that Standard Genetic Programming using standard subtree crossover is prone to a form of structural convergence which makes it extremely difficult to make changes near the root, occasionally causing runs to become trapped in local maxima. Based on these structural limitations we propose a different tree representation, AppGP, which we hope will avoid this problem in some cases...