Concave function

About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.

2-Player nash and nonsymmetric bargaining games: algorithms and structural properties

Abstract: The solution to a Nash or a nonsymmetric bargaining game is obtained by maximizing a concave function over a convex set, i.e., it is the solution to a convex program. We show that each 2-player game whose convex program has linear constraints, admits a rational solution and such a solution can be found in polynomial time using only an LP solver. If in addition, the game is succinct, i.e., the coefficients in its convex program are "small", then its solution can be found in strongly polynomial time. We also give non-succinct linear games whose solution can be found in strongly polynomial time.

Some majorization inequalities for functions of exchangeable random variables

Abstract: : This paper contains inequalities for the exceptions of permutation-invariant concave functions of the partial sums of nonnegative exchangeable random variables. Two majorization inequalities are derived, and an application in reliability theory is discussed. Keywords: Concave and Schurconcave functions.

Concave Darboux Theorem

Abstract: We study the existence of a decomposition of a given germ of 1-form on an affine space as a linear combination with positive coefficients of the differentials of concave functions. The number of entries should be minimal. Necessary and sufficient conditions upon the form germ with regular degeneracy to have such a disaggregation are found. This problem originates from recent papers of P.A. Chiappori and I. Ekeland on the mathematical economy.

Classes of diophantic equations arising in relation to function implementation on microcontrollers

Abstract: We examine the possibilities of easy implementation of functional generators on small microcontrollers and show that the application relates to several classes of equations in natural numbers (Diophantic equations). We define h-easily computable functions to clarify the empirical concept of “easily implemented functions.” The number of concave functions that can be implemented in an easy way on microcontrollers is the main question addressed. The question has relevance, beyond for functional generators, for function approximations on microcontrollers. We provide a framework for the emerged classes of sets of equations and solve a few simple cases. A typical example of equation obtained for such a case is the following equation () 3 33 24 2 4 1 2 (2 1) 2 2 (2 1) 2 (2 2 ) (2 2 ) 2 rr r rr r r r r h ca −⋅ − − = ⋅ ⋅ + − ⋅ − ⋅ , which relates to the design of piecewise linear concave functions on microcontrollers. Similar equations are obtained for npiecewise linear concave functions.