A convex surface contracting by a strictly monotone, homogeneous degree one function of curvature remains smooth until it contracts to a point in finite time, and is asymptotically spherical in shape. No assumptions are made on the concavity of the speed as a function of principal curvatures.

The classical theory of preference among monetary bets represents people as expected utility maximizers with concave utility functions. Critics of this account often rely on assumptions about preferences over wide ranges of total wealth. We derive a prediction of the theory that bears on bets at any fixed level of wealth, and test the prediction behaviorally. Our results are discrepant with the...

Given any two sets of independent non-negative random variables and a non-decreasing concave utility function, we identify sufficient conditions under which the expected utility of sum of these two sets of variables is (almost) equal. We use this result to design a polynomialtime approximation scheme (PTAS) for the utility maximization in a wide variety of risk-averse settings (when the risk a ...

This paper deals with maximization of set f'unctions delined as minimum values of monotone linkage functions. In previous research, it has been shown that such a set function can be maximized by a greedy type algorithm over a family of all subsets of a finite set. ln this paper, we extend this finding to meet-semilattices. We show that the class of functions defined as minimum values of monoton...

Motivated by Schur-concavity, we introduce the notion of G-concavity where G is a closed subgroup of the orthogonal group O(V ) on a finite dimensional real inner product space V . The triple (V,G, F ) is an Eaton triple if F ⊂ V is a nonempty closed convex cone such that (A1) Gx ∩ F is nonempty for each x ∈ V . (A2) maxg∈G(x, gy) = (x, gy) for all x, y ∈ F . If W := spanF and H := {g|W : g ∈ G...

We consider a class of functions satisfying the gross-substitutes property (GS-functions). We show that GS-functions are concave functions, whose parquets are constituted by quasipolymatroids. The class of conjugate functions to GS-functions turns out to be the class of polyhedral supermodular functions. The class of polyhedral GS-functions is a proper subclass of the class of polyhedral submod...

We study multiple unit Discriminative auctions when the bidders share logconcave utility functions and investigate the effects of bidders risk preferences on their bid functions when all bidders share a common utility function and when the bidders exhibit different risk preferences. We extend the existing findings from single unit auctions to multiple unit Discriminative auctions,from concave u...

We examine the Concave Topology Capacity and Flow Assignment (TCFA) problem. Only two algorithms in the literature are appropriate for solving TCFA problems with concave link cost functions: Kleinrock and Gerla’s Concave Branch Elimination (CBE) procedure, [26][20], and a greedy link elimination procedure developed by Gersht [21]. However, neither works well in practice. The CBE procedure does ...

We study equilibrium computation for exchange markets. We show that the market equilibrium of either of the following two markets: 1. The Fisher market with several classes of concave non-homogeneous utility functions; 2. A mixed Fisher and Arrow-Debreu market with homogeneous and log-concave utility functions can be computed as convex programming and by interior-point algorithms in polynomial ...