Primal-dual method for solving a linear-quadratic multi-input optimal control problem

Khimoum, Noureddine; Bibi, Mohand Ouamer

doi:10.1007/s11590-018-1375-2

Cited by 5 publications

(5 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In reality, there are several other factors to take into account and other variables to control. In a future work, we would like to use the support maximum principle [5] , [6] , [10] , as well as the hybrid direction method [25] , to elaborate a primal-dual method for solving a more realistic optimal control problem, in presence of multiple inputs [12] .…”

Section: Discussionmentioning

confidence: 99%

Transport and optimal control of vaccination dynamics for COVID-19

Zaitri

Bibi

Torres

2022

Mathematical Analysis of Infectious Diseases

Self Cite

View full text Add to dashboard Cite

Section: Discussionmentioning

confidence: 99%

Transport and optimal control of vaccination dynamics for COVID-19

Zaitri

Bibi

Torres

2022

Mathematical Analysis of Infectious Diseases

Self Cite

View full text Add to dashboard Cite

“…In reality, there are several other factors to have into account and other variables to control. In a future work, we would like to use the support maximum principle [5,6,10], as well as the hybrid direction method [25], to elaborate a primal-dual method for solving a more realistic optimal control problem, in presence of multiple inputs [12].…”

Section: Discussionmentioning

confidence: 99%

Transport and Optimal Control of Vaccination Dynamics for COVID-19

Zaitri,

Bibi,

Torres

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We develop a mathematical model for transferring the vaccine BNT162b2 based on the heat diffusion equation. Then, we apply optimal control theory to the proposed generalized SEIR model. We introduce vaccination for the susceptible population to control the spread of the COVID-19 epidemic. For this, we use the Pontryagin minimum principle to find the necessary optimality conditions for the optimal control. The optimal control problem and the heat diffusion equation are solved numerically. Finally, several simulations are done to study and predict the spread of the COVID-19 epidemic in Italy. In particular, we compare the model in the presence and absence of vaccination.

show abstract

“…Later, they have developed the adaptive method, 2,3 which uses a direction depending on the current solution. This method is applied later to solve optimal control problems and generalized for solving linear and convex quadratic problems 4‐9 …”

Section: Introductionmentioning

confidence: 99%

“…This method is applied later to solve optimal control problems and generalized for solving linear and convex quadratic problems. [4][5][6][7][8][9] In References 10-13, a new algorithm for solving linear programming problems with bounded variables was developed. This algorithm uses the concept of hybrid direction in order to move from one feasible solution to a better one.…”

Section: Introductionmentioning

confidence: 99%

A new method with hybrid direction for linear programming

Djeloud

Bentobache

Bibi

2020

Concurrency and Computation

Self Cite

View full text Add to dashboard Cite

Summary In this work, we propose a new algorithm for solving linear programs. This algorithm starts by an initial support feasible solution, then it moves from one feasible point to a better one following a new hybrid direction. The constructed direction gives a better local improvement of the objective function than the direction of the adaptive method with hybrid direction (AMHD) algorithm proposed in Bibi MO, Bentobache M. A hybrid direction algorithm for solving linear programs. International Journal of Computer Mathematics, 2015; 92(2):200‐216. In order to stop the algorithm, a suboptimality criterion is used and the long step rule is developed for changing the current support. The proposed algorithm is implemented with C++, then a numerical study is conducted on randomly generated test problems and some instances of an optimal control problem. The obtained numerical results show that our algorithm is competitive with AMHD and the primal simplex algorithm of GNU linear programming kit (GLPK).

show abstract

Primal-dual method for solving a linear-quadratic multi-input optimal control problem

Cited by 5 publications

References 25 publications

Transport and optimal control of vaccination dynamics for COVID-19

Transport and optimal control of vaccination dynamics for COVID-19

Transport and Optimal Control of Vaccination Dynamics for COVID-19

A new method with hybrid direction for linear programming

Contact Info

Product

Resources

About