We provide two new, simple proofs of Afriat's celebrated theorem stating that a finite set of price-quantity observations is consistent with utility maximization if, and only if, the observations satisfy a variation of the Strong Axiom of Revealed Preference known as the Generalized Axiom of...

I Brouwer’s Theorem -- II Some Applications of Brouwer’s Theorem -- III Triangulations -- IV Algorithms to Find Completely-Labelled Simplices -- V Extensions of Brouwer’s Theorem -- VI Applications of Kakutani’s Theorem and its Extensions -- VII Eaves’ First Algorithm -- VIII...

Includes bibliographical references (p. 37-39).

We describe a projective algorithm for linear programming that shares features with Karmarkar's projective algorithm and its variants and with the path-following methods of Gonzaga, Kojima-Mizuno-Yoshise, Monteiro-Adler, Renegar, Vaidya and Ye. It operates in a primal-dual setting, stays close...