A Modified Super Convergent Line Series Algorithm for Solving Unconstrained Optimization Problems

Umoren, M. U.; Etukudo, Idorenyin

doi:10.3923/jmmstat.2010.115.122

Cited by 6 publications

(4 citation statements)

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“…To design an experiment optimally, we mean a selection of N support points within the experimental region so that the aim of the experimenter could be realized. Unlike RSM where the step length is obtained by trial and error, [9] had already modified an algorithm by [10] to solve an unconstrained optimization problems using the principle of optimal designs of experiment where the step length is obtained by taking the derivative of the response function. As by [9], a well-defined method to handle interactive effects in the case of quadratic surfaces has been provided.…”

Section: Introductionmentioning

confidence: 99%

“…Since this new technique is a line search algorithm, it relies on a well-defined method of determining the direction of search as given by [11]. The algorithmic procedure which is given in the next section requires that the optimal support points that form the initial design matrix obtained from the entire experimental region be partitioned into r groups, 2,3, , r k =  .…”

Section: Introductionmentioning

confidence: 99%

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Optimal Designs Technique for Locating the Optimum of a Second Order Response Function

Etukudo¹

2017

AJOR

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A more efficient method of locating the optimum of a second order response function was of interest in this work. In order to do this, the principles of optimal designs of experiment is invoked and used for this purpose. At the end, it was discovered that the noticeable pitfall in response surface methodology (RSM) was circumvented by this method as the step length was obtained by taking the derivative of the response function rather than doing so by intuition or trial and error as is the case in RSM. A numerical illustration shows that this method is suitable for obtaining the desired optimizer in just one move which compares favourably with other known methods such as Newton-Raphson method which requires more than one iteration to reach the optimizer.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Designs Technique for Locating the Optimum of a Second Order Response Function

Etukudo¹

2017

AJOR

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“…This new technique was brought about from super convergent line series algorithm which uses the principles of optimal designs of experiment [11] [12] and as modified by [13] (see also [14] and [15]). The algorithmic procedure used in realizing our objective in this work is as given by [10].…”

Section: Introductionmentioning

confidence: 99%

The Optimum of a Quadratic Univariate Response Function Is Located at the Origin

Etukudo¹

2017

AJOR

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“…The initial design measure for the Maximum Norm Exchange Algorithm consists of design points selected from the boundary of the design region. Other works that apply experimental design principles for solving optimization problems include Umoren and Etukudo (2010), Osita and Iwundu (2013), Ekezie and Nzenwa (2013), Chigbu and Ukaegbu (2013), Ekezie etal. (2013), Iwundu and Hezekiah (2014), Iwundu and Ebong (2014) and Iwundu and Ndiyo (2015).…”

Section: Introductionmentioning

confidence: 99%

Rules for Identifying the Initial Design Points for Use in the Quick Convergent Inflow Algorithm

Iwundu¹,

Ekpo²

2015

IJSP

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The starting point of search is an important factor in optimal design construction as a poor starting point may require a longer time before convergence is reached. Hence the location of the initial design points for use in the Quick Convergent Inflow Algorithm on segmented regions is examined with the aim of developing useful criteria for identifying the initial design points. Proportional allocation of design points to go into the initial design measures is proposed. The allocation of 100% vertex points, 100% boundary points and 100% boundary points as well as the allocation of 50% vertex and 50% boundary points, 50% vertex and 50% interior points and 50% interior and 50% boundary points are investigated. Results show that a combination of design points comprising of 50% vertex points and 50% interior points or 50% vertex points and 50% boundary points forms helpful rules in identifying the initial design points for use in the Quick Convergent Inflow Algorithm. With these combinations, a moderate number of iterations needed to reach the required optimal or near-optimal solution is maintained.

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A Modified Super Convergent Line Series Algorithm for Solving Unconstrained Optimization Problems

Cited by 6 publications

References 0 publications

Optimal Designs Technique for Locating the Optimum of a Second Order Response Function

Optimal Designs Technique for Locating the Optimum of a Second Order Response Function

The Optimum of a Quadratic Univariate Response Function Is Located at the Origin

Rules for Identifying the Initial Design Points for Use in the Quick Convergent Inflow Algorithm

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