ANALYSIS OF SPLIT BREGMAN METHOD FOR SOLVING THE OPTIMAL CONTROL PROBLEM WITH ELLIPTIC PARTIAL DIFFERENTIAL EQUATION CONSTRAINT

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LOTFI HONYANDARI MAHMOUD; HOSSEINI SEYED MOHAMMAD

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Journal: JOURNAL OF SCIENCE (KHARAZMI UNIVERSITY) Year:2014 | Volume:14 | Issue:2 Page(s): 115-126

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Title

ANALYSIS OF SPLIT BREGMAN METHOD FOR SOLVING THE OPTIMAL CONTROL PROBLEM WITH ELLIPTIC PARTIAL DIFFERENTIAL EQUATION CONSTRAINT

Author(s)

LOTFI HONYANDARI MAHMOUD | HOSSEINI SEYED MOHAMMAD | Issue Writer Certificate

Keywords

OPTIMAL CONTROL WITH ELLIPTIC PARTIAL DIFFERENTIAL EQUATION CONSTRAINTQ2

FINITE ELEMENT METHODQ2

SPLIT BREGMAN METHODQ2

Abstract

In recent decades optimal control problems with partial differential equation constraints have been studied extensively. These issues are very complex and the numerical solution of such problems is of great importance. In this article we will discuss the solution of elliptic optimal control problem. First, by using the FINITE ELEMENT METHOD we obtain to gain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory.But split Bergman method converts the constrained problem to an unconstrained problem, and hence it saves time and memory requirement. We then use the split Bergman iterative methods for solving this problem, and examples show the speed and accuracy of split Bergman iterative methods for solving this type of problems. We also use the SQP method for solving the problem and compare with split Bergman method.

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APA: Copy

LOTFI HONYANDARI, MAHMOUD, & HOSSEINI, SEYED MOHAMMAD. (2014). ANALYSIS OF SPLIT BREGMAN METHOD FOR SOLVING THE OPTIMAL CONTROL PROBLEM WITH ELLIPTIC PARTIAL DIFFERENTIAL EQUATION CONSTRAINT. JOURNAL OF SCIENCE (KHARAZMI UNIVERSITY), 14(2), 115-126. SID. https://sid.ir/paper/43995/en

Vancouver: Copy

LOTFI HONYANDARI MAHMOUD, HOSSEINI SEYED MOHAMMAD. ANALYSIS OF SPLIT BREGMAN METHOD FOR SOLVING THE OPTIMAL CONTROL PROBLEM WITH ELLIPTIC PARTIAL DIFFERENTIAL EQUATION CONSTRAINT. JOURNAL OF SCIENCE (KHARAZMI UNIVERSITY)[Internet]. 2014;14(2):115-126. Available from: https://sid.ir/paper/43995/en

IEEE: Copy

MAHMOUD LOTFI HONYANDARI, and SEYED MOHAMMAD HOSSEINI, “ANALYSIS OF SPLIT BREGMAN METHOD FOR SOLVING THE OPTIMAL CONTROL PROBLEM WITH ELLIPTIC PARTIAL DIFFERENTIAL EQUATION CONSTRAINT,” JOURNAL OF SCIENCE (KHARAZMI UNIVERSITY), vol. 14, no. 2, pp. 115–126, 2014, [Online]. Available: https://sid.ir/paper/43995/en

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