Improvement of time complexity of homotopy with 2-step predictor-corrector method

Kerk, Lee Chang; Ahmad, Rohanin

doi:10.1063/1.4980945

Cited by 3 publications

(4 citation statements)

References 3 publications

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“…Table 2 shows the mean return for each asset generated from the fund data where r1 represents the mean return for y 1 , r2 represents the mean return for y 2 , r3 represents the mean return for y 3 and r4 represents the mean return for y 4 . Meanwhile, the matrix of variancecovariance was computed using Equations ( 4) and (5). Then, the objective function was formed with Equation ( 7), yielding the minimize F in Equation (9).…”

Section: Resultsmentioning

confidence: 99%

“…and the covariance of assets i and k could be represented by Equation (5). Then, the portfolio risk could be defined by Equation (6).…”

Section: Problem Description and Methodologymentioning

confidence: 99%

“…Subsequently, an algorithm known as homotopy with two-step predictor-corrector method (HSPM) was developed by Kerk to overcome the computational burden of HOPE [5]. Although HSPM performed better than HOPE in time of complexity, it was designed to solve the one variable optimization problem only.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global Optimization Method For Minimizing Portfolio Selection Risk

Kerk,

Mokhtar,

Shamala

et al. 2022

MATEMATIKA

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This study employed the global optimization method called Modified Trusted Region Method (MTRM) to resolve the portfolio selection risk problem. An objective of unconstrained optimization problem was formulated with four sets of fund data. The relationship between the level of acceptable risk and the weighting factor was analyzed numerically. The return of portfolio increased along with the level of acceptable risk since a high return was always accompanied by higher risk. By contrast, the risk of portfolio decreased as the weighting factor increased. The MTRM could resolve the portfolio optimization problem.

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Section: Resultsmentioning

confidence: 99%

“…and the covariance of assets i and k could be represented by Equation (5). Then, the portfolio risk could be defined by Equation (6).…”

Section: Problem Description and Methodologymentioning

confidence: 99%

See 1 more Smart Citation

Global Optimization Method For Minimizing Portfolio Selection Risk

Kerk,

Mokhtar,

Shamala

et al. 2022

MATEMATIKA

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“…However, RS, DE, NM and SA only found the one of the six solutions while HSPM and I-HSPM located all of them. I-HSPM is an improved method from HSPM and shown has a better time complexity than HSPM [26]. Here, their CPU time will be compared by using the parameter s = 0.003 to divide the domain into several sub-intervals.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Algorithm for Solution of Non-convex Optimization Problem Through Piece-wise Convex Transformation

Kerk

Ahmad

2018

MATEMATIKA

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Optimization is central to any problem involving decision making. Thearea of optimization has received enormous attention for over 30 years and it is still popular in research field to this day. In this paper, a global optimization method called Kerk and Rohanin’s Trusted Interval will be introduced. The method introduced is able to identify all local solutions by converting non-convex optimization problems into piece-wise convex optimization problems. A mechanism which only considers the convex part where minimizers existed on a function is applied. This mechanism allows the method to filter out concave parts and some unrelated parts automatically. The identified convex parts are called trusted intervals. The descent property and the globally convergent of the method was shown in this paper. 15 test problems have been used to show the ability of the algorithm proposed in locating global minimizer.

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A robust algorithm for global optimization problems

Kerk

Lau

Ahmad

et al. 2021

J. Phys.: Conf. Ser.

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In this paper, a global optimization algorithm namely Kerk and Rohanin’s Trusted Region is used to find the global minimizers by employing an interval technique; with it, the algorithm can find the region where a minimizer is located and will not get trapped in a local one. It is able to find the convex part within the non-convex feasible region. This algorithm has descent property and global convergence. The numerical results have shown the algorithm has an outstanding capability in locating global minimizers.

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Improvement of time complexity of homotopy with 2-step predictor-corrector method

Cited by 3 publications

References 3 publications

Global Optimization Method For Minimizing Portfolio Selection Risk

Global Optimization Method For Minimizing Portfolio Selection Risk

Algorithm for Solution of Non-convex Optimization Problem Through Piece-wise Convex Transformation

A robust algorithm for global optimization problems

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