1,250 research outputs found
Inertial game dynamics and applications to constrained optimization
Aiming to provide a new class of game dynamics with good long-term
rationality properties, we derive a second-order inertial system that builds on
the widely studied "heavy ball with friction" optimization method. By
exploiting a well-known link between the replicator dynamics and the
Shahshahani geometry on the space of mixed strategies, the dynamics are stated
in a Riemannian geometric framework where trajectories are accelerated by the
players' unilateral payoff gradients and they slow down near Nash equilibria.
Surprisingly (and in stark contrast to another second-order variant of the
replicator dynamics), the inertial replicator dynamics are not well-posed; on
the other hand, it is possible to obtain a well-posed system by endowing the
mixed strategy space with a different Hessian-Riemannian (HR) metric structure,
and we characterize those HR geometries that do so. In the single-agent version
of the dynamics (corresponding to constrained optimization over simplex-like
objects), we show that regular maximum points of smooth functions attract all
nearby solution orbits with low initial speed. More generally, we establish an
inertial variant of the so-called "folk theorem" of evolutionary game theory
and we show that strict equilibria are attracting in asymmetric
(multi-population) games - provided of course that the dynamics are well-posed.
A similar asymptotic stability result is obtained for evolutionarily stable
strategies in symmetric (single- population) games.Comment: 30 pages, 4 figures; significantly revised paper structure and added
new material on Euclidean embeddings and evolutionarily stable strategie
Analysis of some interior point continuous trajectories for convex programming
In this paper, we analyse three interior point continuous trajectories for convex programming with general linear constraints. The three continuous trajectories are derived from the primal–dual path-following method, the primal–dual affine scaling method and the central path, respectively. Theoretical properties of the three interior point continuous trajectories are fully studied. The optimality and convergence of all three interior point continuous trajectories are obtained for any interior feasible point under some mild conditions. In particular, with proper choice of some parameters, the convergence for all three interior point continuous trajectories does not require the strict complementarity or the analyticity of the objective function. These results are new in the literature
On the convergence of the affine-scaling algorithm
Cover title.Includes bibliographical references (p. 20-22).Research partially supported by the National Science Foundation. NSF-ECS-8519058 Research partially supported by the U.S. Army Research Office. DAAL03-86-K-0171 Research partially supported by the Science and Engineering Research Board of McMaster University.by Paul Tseng and Zhi-Quan Luo
On the Convergence of the Mizuno-Todd-Ye Algorithm to the Analytic Center of the Solution Set
In this work we demonstrate that the Mizuno-Todd-Ye predictor corrector primal-dual interior-point method for linear programming generates iteration sequences that converge to the analytic center of the solution set
- …