A global optimization approach to fractional optimal control

In this paper, we consider a fractional optimal control problem governed by system of linear differential equations, where its cost function is expressed as the ratio of convex and concave functions. The problem is a hard nonconvex optimal control problem and application of Pontriyagin's principle does not always guarantee finding a global optimal control. Even this type of problems in a finite dimensional space is known as NP hard. This optimal control problem can, in principle, be solved by Dinkhelbach algorithm [10]. However, it leads to solving a sequence of hard D.C programming problems in its finite dimensional analogy. To overcome this difficulty, we introduce a reachable set for the linear system. In this way, the problem is reduced to a quasiconvex maximization problem in a finite dimensional space. Based on a global optimality condition, we propose an algorithm for solving this fractional optimal control problem and we show that the algorithm generates a sequence of local optimal controls with improved cost values. The proposed algorithm is then applied to several test problems, where the global optimal cost value is obtained for each case

General models in min-max continous location

In this paper, a class of min-max continuous location problems is discussed. After giving a complete characterization of th stationary points, we propose a simple central and deep-cut ellipsoid algorithm to solve these problems for the quasiconvex case. Moreover, an elementary convergence proof of this algorithm and some computational results are presented

La convexité généralisée en économie mathématique

We show that generalized convexity appears quite naturally in some models of mathematical economics, specially in the consumer's behaviour theory

Pseudomonotonicity of an affine map and the two dimensional case

In this paper the pseudomonotonicity of the affine map F(x) = Mx+q on the interior of the positive orthant of Rn is studied. A new characterization is suggested involving the positive and the negative polar of the cone generated by the set W*={z=Mx+q: x∈ intRn +}. The obtained results are applied to the two dimensional case in order to achieve a complete characterization of pseudomonotonicity in terms of the coefficients of M and q