This paper investigates the problem of maximizing the revenue of a telecommunications operator by simultaneously pricing point-to-point services and allocating bandwidth in its network, while facing competition. Customers are distributed into market segments, i.e., groups of customers with a similar preference for the services. This preference is expressed using utility functions, and customers choose between the offers of the operator and of the competition according to their utility. We model the problem as a leader-follower game between the operator and the customers. This kind of problem has classically been modeled as a bilevel program. A market segmentation is usually defined by a discrete distribution function of the total demand for a service; in this case, the problem can be modeled as a combinatorial optimization problem. In this paper, however, we motivate the use of a continuous distribution function and investigate the nonlinear continuous optimization problem obtained in this case. We analyze the mathematical properties of the problem, and in particular we give a necessary and sufficient condition for its convexity. We introduce methods to solve the problem and we provide encouraging numerical results on realistic telecommunications instances of the problem, showing that it can be solved efficiently.

The aim of this paper is to show a polynomial algorithm for the problem minimum directed sumcut for a class of series parallel digraphs. The method uses the recursive structure of parallel compositions in order to define a dominating set of orders. Then, the optimal order is easily reached by minimizing the directed sumcut. It is also shown that this approach cannot be applied in two more general classes of series parallel digraphs.

This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0–1 problems. Furthermore, its tractability is highlighted. Then, an optimization algorithm is designed to provide possibly good solutions to chance-constrained combinatorial problems. This approach is numerically tested on knapsack and multi-dimensional knapsack problems. The results obtained outperform many methods based on earlier literature.

Recently, Y.Q. Bai, M. El Ghami and C. Roos [3] introduced a new class ofso-called eligible kernel functions which are defined by somesimple conditions.The authors designed primal-dual interior-point methods for linear optimization (LO)based on eligible kernel functionsand simplified the analysis of these methods considerably.In this paper we consider the semidefinite optimization (SDO) problemand we generalize the aforementioned results for LO to SDO.The iteration bounds obtained are analogous to the results in [3] for LO.

In this work, we study an optimal control problem dealing with differential inclusion.Without requiring Lipschitz condition of the set valued map, it isvery hard to look for a solution of the control problem. Our aim isto find estimations of the minimal value, (α), of the costfunction of the control problem. For this, we construct anintermediary dual problem leading to a weak duality result, andthen, thanks to additional assumptions of monotonicity of proximalsubdifferential, we give a more precise estimation of (α). Onthe other hand, when the set valued map fulfills the Lipshitzcondition, we prove that the lower semicontinuous (l.s.c.) proximalsupersolutions of the Hamilton-Jacobi-Bellman (HJB) equationcombined with the estimation of (α), lead to a sufficientcondition of optimality for a suspected trajectory. Furthermore, weestablish a strong duality between this optimal control problem anda dual problem involving upper hull of l.s.c. proximalsupersolutions of the HJB equation (respectively with contingentsupersolutions). Finally this strong duality gives rise to necessaryand sufficient conditions of optimality.

Two games are inseparable by semivalues if both gamesobtain the same allocation whatever semivalue is considered. The problem ofseparability by semivalues reduces to separability from the nullgame. For four or more players, the vector subspace of gamesinseparable from the null game by semivalues contains gamesdifferent to zero-game. Now, for five or more players, theconsideration of a priori coalition blocks in the player set allowsus to reduce in a significant way the dimension of the vectorsubspace of games inseparable from the null game. For thesesubspaces we provide basis formed by games of a particular type.