Nonlinear programming approach for a transient free boundary flow problem

Chakib, Abdelkrim; Nachaoui, Abdeljalil

doi:10.1016/j.amc.2003.08.101

Cited by 10 publications

(20 citation statements)

References 5 publications

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“…To solve this nonlinear mathematical programming we use the sequential quadratic programming. Numerical results for illustrative earth dam problems are discussed (Chakib and Nachaoui, 2005).…”

Section: Literature Reviewmentioning

confidence: 99%

A Nash bargaining game data envelopment analysis model for measuring efficiency of dynamic multi-period network structures

Gazori-Nishabori

Khalili‐Damghani

Hafezalkotob

2022

JM2

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Purpose A Nash bargaining game data envelopment analysis (NBG-DEA) model is proposed to measure the efficiency of dynamic multi-period network structures. This paper aims to propose NBG-DEA model to measure the performance of decision-making units with complicated network structures. Design/methodology/approach As the proposed NBG-DEA model is a non-linear mathematical programming, finding its global optimum solution is hard. Therefore, meta-heuristic algorithms are used to solve non-linear optimization problems. Fortunately, the NBG-DEA model optimizes the well-formed problem, so that it can be solved by different non-linear methods including meta-heuristic algorithms. Hence, a meta-heuristic algorithm, called particle swarm optimization (PSO) is proposed to solve the NBG-DEA model in this paper. The case study is Industrial Management Institute (IMI), which is a leading organization in providing consulting management, publication and educational services in Iran. The sub-processes of IMI are considered as players where their pay-off is defined as the efficiency of sub-processes. The network structure of IMI is studied during multiple periods. Findings The proposed NBG-DEA model is applied to measure the efficiency scores in the IMI case study. The solution found by the PSO algorithm, which is implemented in MATLAB software, is compared with that generated by a classic non-linear method called gradient descent implemented in LINGO software. Originality/value The experiments proved that suitable and feasible solutions could be found by solving the NBG-DEA model and shows that PSO algorithm solves this model in reasonable central process unit time.

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Section: Literature Reviewmentioning

confidence: 99%

A Nash bargaining game data envelopment analysis model for measuring efficiency of dynamic multi-period network structures

Gazori-Nishabori

Khalili‐Damghani

Hafezalkotob

2022

JM2

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“…If we assume w = u − U 0 ∈ H D (Ω), now the shape optimization problem (6)- (7) reduces to the following optimization problem in homogeneous form:…”

Section: Lemmamentioning

confidence: 99%

“…for all ϕ ∈ U ad , where u ϕ is solution of the state problem (7). Let H D (Ω) be the space defined by:…”

Section: Lemmamentioning

confidence: 99%

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Filtration problem in inhomogeneous dam by using embedding method

Nazemi

Farahi

Zamirian

2008

J. Appl. Math. Comput.

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This paper is devoted to a new numerical technique for the approximation of the flow problem of incompressible liquid through an inhomogeneous porous medium (say dam). First the problem is expressed as an optimal control problem governed by variational forms on a fixed domain. Then by using an embedding method, the class of admissible shapes is replaced by a class of positive Radon measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this linear programming problem. Numerical example is also given.

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“…During the optimization process the optimal solution is obtained in an iterative manner, by solving several intermediate direct problems. In section 4 we use the boundary element method which is a very appropriate tool to solve these intermediate problems (see, for example, [4]). This approximation leads to fully populated matrices which, in general, are not symmetric and not positive definite.…”

Section: Introductionmentioning

confidence: 99%

Parallel solvers for the depletion region identification in metal semiconductor field effect transistors

2005

Self Cite

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In this work we are interested in a sufficiently accurate approximation of the steady-state potentials in a Metal Semiconductor Field Effect Transistor (MESFET), which can be obtained with the so-called depletion region approximation (see [5]). We propose a robust method based on the shape optimization techniques to analyze and compute the depletion boundary as a function of the applied voltage and the geometry material properties of the device. During the optimization process several intermediate direct problems are solved using the boundary element method (BEM). To accelerate the solutions of of these systems we use a strategy of subdividing the domain into a number of smaller subdomains [11,9]. The scheme is iterative and each subdomain is handled by a separate node in parallel. Test runs comparing the performance of the parallel with the serial code, and other numerical discussions are presented.

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Nonlinear programming approach for a transient free boundary flow problem

Cited by 10 publications

References 5 publications

A Nash bargaining game data envelopment analysis model for measuring efficiency of dynamic multi-period network structures

A Nash bargaining game data envelopment analysis model for measuring efficiency of dynamic multi-period network structures

Filtration problem in inhomogeneous dam by using embedding method

Parallel solvers for the depletion region identification in metal semiconductor field effect transistors

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