We consider a general-sum N-player linear-quadratic game with stochastic dynamics over finite horizon and prove the global convergence of natural policy gradient method to Nash equilibrium. In order we require certain amount noise in system. give condition, essentially lower bound on covariance terms model parameters, guarantee convergence. illustrate our results numerical experiments show that...

long time integration of large stiff systems of initial value problems, arising from chemical reactions, demands efficient methods with good accuracy and extensive absolute stability region. in this paper, we apply second derivative general linear methods to solve some stiff chemical problems such as chemical akzo nobel problem, hires problem and orego problem.

In this paper, the constrained M-estimation of the regression coefficients and scatter parameters in a multivariate linear regression model is considered. Robustness and asymptotic behavior are investigated. Since constrained M-estimation is not easy to compute, an up-dating recursion procedure is proposed to simplify the computation of the estimators when a new observation is obtained. We show...

Much effort is put into the construction of general linear methods with the aim of achieving an excellent long-time behavior for the integration of Hamiltonian systems. In this article, a backward error analysis is presented, which permits to get sharp estimates for the parasitic solution components and for the error in the Hamiltonian. For carefully constructed methods (symmetric and zero grow...

‎we describe the construction of second derivative general linear methods (sglms) of orders five and six‎. ‎we will aim for methods which are a--stable and have runge--kutta stability property‎. ‎some numerical results are given to show the efficiency of the constructed methods in solving stiff initial value problems‎.

G-symplectic general linear methods are designed to approximately preserve symplectic invariants for Hamiltonian systems. In this paper, the properties of G-symplectic methods are explored computationally and theoretically. Good preservation properties are observed over long times for many parameter ranges, but, for other parameter values, the parasitic behavior, to which multivalue methods are...

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

Fmoc-amino acids were obtained from GL Biochem (Shanghai, China). All the other Starting materials were obtained from Alfa. Chemical reagents and solvents were used as received from commercial sources.