We show how the classical Lagrangian approach to solving constrained optimization problems from standard calculus can be extended to solve continuous time stochastic optimal control problem. Connections to mainstream approaches such as the Hamilton-Jacobi-Bellman equation and the stochastic...

In this paper, we propose a new approach for stochastic control problems arising from utility maximization. The main idea is to directly start from the dynamical programming equation and compute the conditional expectation using a novel representation of the conditional density function through...

We study scheduling in a stochastic processing network where there are multiple job types, multiple homogeneous servers, and jobs are expressed as directed acyclic graphs (DAGs) of tasks. Our main motivation is the scheduling of cloud computing resources where customers express their requests as...

In this article, we propose a PEARM mathematical model to depict the dynamic of a population that reacts in the spread of the gaming disorder with media coverage. The basic reproduction number and existence of free equilibrium point and endimec equilibrium point are obtained with same...

The efficacy of the widely-adopted “top-n” policy in university integration has been questioned because students strategically relocate to low-achieving high schools. We show that when different SES groups have heterogenous relocation costs, the policy can even segregate minorities from the...

In this paper, we present several optimal control approaches which are designed to control and regulate the evolution of infection numbers in the COVID-19 disease. In our setting, the number of infected people at a certain location is modeled by a continuous-time stochastic process which can be...

In this paper, to investigate the synthetic effffect of PrEP (pre-exposure prophylaxis) and ART (antiretrovial therapy) on HIV transmission among MSM (men who have sex with men) in heterogenous environment, an realistic HIV epidemic model with spatial diffusion is established. Here, HIV...

In order to solve the problem of grid voltage fluctuations in multi-energy systems. This paper proposes a coordinated optimization control method based on battery electric storage, heat storage, and gas storage. Firstly, analyzing the different operating modes of electricity, heat, and gas in...