Effort Maximization in Asymmetric N-person Contest Games

This paper provides existence and characterization of the optimal contest success function under the condition that the objective of the contest designer is total effort maximization among n heterogeneous players. Heterogeneity of players makes active participation of a player in equilibrium endogenous with respect to the specific contest success function adopted by the contest designer. Hence, the aim of effort maximization implies the identification of those players who should be excluded from making positive efforts.We give a general proof for the existence of an optimal contest success function and provide an algorithm for the determination of the set of actively participating players.This is turn allows to determine optimal efforts in closed form.An important general feature of the solution is that maximization of total effort requires at least three players to be active.Effort maximization, existence of solution, asymmetric contests, participation constraints

Effort Maximization in Asymmetric N-Person Contest Games

This paper provides existence and characterization of the optimal contest success function under the condition that the objective of the contest designer is total effort maximization among n heterogeneous players. Heterogeneity of players makes active participation of a player in equilibrium endogenous with respect to the specific contest success function adopted by the contest designer. Hence, the aim of effort maximization implies the identification of those players who should be excluded from making positive efforts. We give a general proof for the existence of an optimal contest success function and provide an algorithm for the determination of the set of actively participating players. This is turn allows to determine optimal efforts in closed form. An important general feature of the solution is that maximization of total effort requires at least three players to be active.effort maximization, existence of solution, asymmetric contests, participation constraints

Generalized Stationary Points and an Interior Point Method for MPEC

Mathematical program with equilibrium constraints (MPEC)has extensive applications in practical areas such as traffic control, engineering design, and economic modeling. Some generalized stationary points of MPEC are studied to better describe the limiting points produced by interior point methods for MPEC.A primal-dual interior point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced without assuming strict complementarity or linear independence constraint qualification. Under very general assumptions, the algorithm can always find some point with strong or weak stationarity. In particular, it is shown that every limiting point of the generated sequence is a piece-wise stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a certain point with weak stationarity can be obtained. Preliminary numerical results are satisfactory, which include a case analyzed by Leyffer for which the penalty interior point algorithm failed to find a stationary solution.Singapore-MIT Alliance (SMA

A globally convergent neurodynamics optimization model for mathematical programming with equilibrium constraints

summary:This paper introduces a neurodynamics optimization model to compute the solution of mathematical programming with equilibrium constraints (MPEC). A smoothing method based on NPC-function is used to obtain a relaxed optimization problem. The optimal solution of the global optimization problem is estimated using a new neurodynamic system, which, in finite time, is convergent with its equilibrium point. Compared to existing models, the proposed model has a simple structure, with low complexity. The new dynamical system is investigated theoretically, and it is proved that the steady state of the proposed neural network is asymptotic stable and global convergence to the optimal solution of MPEC. Numerical simulations of several examples of MPEC are presented, all of which confirm the agreement between the theoretical and numerical aspects of the problem and show the effectiveness of the proposed model. Moreover, an application to resource allocation problem shows that the new method is a simple, but efficient, and practical algorithm for the solution of real-world MPEC problems

Validation of nominations in gas networks and properties of technical capacities

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Contributions to complementarity and bilevel programming in Banach spaces

In this thesis, we derive necessary optimality conditions for bilevel programming problems (BPPs for short) in Banach spaces. This rather abstract setting reflects our desire to characterize the local optimal solutions of hierarchical optimization problems in function spaces arising from several applications. Since our considerations are based on the tools of variational analysis introduced by Boris Mordukhovich, we study related properties of pointwise defined sets in function spaces. The presence of sequential normal compactness for such sets in Lebesgue and Sobolev spaces as well as the variational geometry of decomposable sets in Lebesgue spaces is discussed. Afterwards, we investigate mathematical problems with complementarity constraints (MPCCs for short) in Banach spaces which are closely related to BPPs. We introduce reasonable stationarity concepts and constraint qualifications which can be used to handle MPCCs. The relations between the mentioned stationarity notions are studied in the setting where the underlying complementarity cone is polyhedric. The results are applied to the situations where the complementarity cone equals the nonnegative cone in a Lebesgue space or is polyhedral. Next, we use the three main approaches of transforming a BPP into a single-level program (namely the presence of a unique lower level solution, the KKT approach, and the optimal value approach) to derive necessary optimality conditions for BPPs. Furthermore, we comment on the relation between the original BPP and the respective surrogate problem. We apply our findings to formulate necessary optimality conditions for three different classes of BPPs. First, we study a BPP with semidefinite lower level problem possessing a unique solution. Afterwards, we deal with bilevel optimal control problems with dynamical systems of ordinary differential equations at both decision levels. Finally, an optimal control problem of ordinary or partial differential equations with implicitly given pointwise state constraints is investigated