New technique for solving univariate global optimization

Aaid, Djamel; Noui, Amel; Ouanes, Mohand

doi:10.5817/am2017-1-19

Cited by 3 publications

(6 citation statements)

References 21 publications

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“…Piecewise Quadratic Bounds. Considering definition of the lower bound, the upper bound was constructed in [1] similarly. Assume that X = [a, b] be a bounded closed interval in R and f be a continuous differentiable polynomial with second degree on X.…”

Section: The Concavity and Convexity Test Detects The Regions Whethermentioning

confidence: 99%

“…First, we divide the closed interval [0, 2] into the two equal parts such as [0, 1] and [1,2]. If we apply our method (concave convex test) on to f polynomial, we get f ([0, 1]) ≤ 0 implies that f is concave on [0, 1] and also {0, 1} is the set of roots of f due to the solutions of U 1 (x) = 0.…”

Section: Illustrative Examplementioning

confidence: 99%

“…Besides, we have f ([1, 2]) ≥ 0. This gives that f is convex on [1,2] and {1, 2} is the set of roots of f because of the solutions of L 2 (x) = 0. Therefore, the polynomial has only three roots as 0,1 and 2.…”

Section: Illustrative Examplementioning

confidence: 99%

“…In [1,8,7], D. Aaid et al proposed an approximation to obtain a global minimum of the univariate objective function. C. S. Adjiman and his co-authors created/constructed a based Branch and Bound global optimization useful on the bounds of global minimum in [2].…”

mentioning

confidence: 99%

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Piecewise quadratic bounding functions for finding real roots of polynomials

Aaid¹,

Noui²,

Özer³

2021

NACO

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In this paper, our main interest is to create/ construct a new useful and outstanding algorithm to obtain roots of the real polynomial represented by f (x) = c 0 + c 1 x + ... + c i x i + ... + cnx n where coefficients of the polynomials are real numbers and x is a real number in the closed interval of R. Also, our results are supported by numerical examples. Then, a new algorithm is compared with the others (writer classical methods) and this algorithm is more useful than others.

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Section: The Concavity and Convexity Test Detects The Regions Whethermentioning

confidence: 99%

Section: Illustrative Examplementioning

confidence: 99%

Section: Illustrative Examplementioning

confidence: 99%

mentioning

confidence: 99%

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Piecewise quadratic bounding functions for finding real roots of polynomials

Aaid¹,

Noui²,

Özer³

2021

NACO

Self Cite

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show abstract

“…As "what is the best technique to find global optimum?" [28], [29] is still an open question, we measured the runtime of our algorithms in term of how many times they have to query for finding global optimum of a univariate function.…”

Section: Algorithm 4 Full Set Interdictionmentioning

confidence: 99%

Length-Bounded Paths Interdiction in Continuous Domain for Network Performance Assessment

Nguyen¹,

Thai²

2020

Preprint

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Studying on networked systems, in which a communication between nodes is functional if their distance under a given metric is lower than a pre-defined threshold, has received significant attention recently. In this work, we propose a metric to measure network resilience on guaranteeing the pre-defined performance constraint. This metric is investigated under an optimization problem, namely Length-bounded Paths Interdiction in Continuous Domain (cLPI), which aims to identify a minimum set of nodes whose changes cause routing paths between nodes become undesirable for the network service.We show the problem is NP-hard and propose a framework by designing two oracles, Threshold Blocking (TB) and Critical Path Listing (CPL), which communicate back and forth to construct a feasible solution to cLPI with theoretical bicriteria approximation guarantees. Based on this framework, we propose two solutions for each oracle. Each combination of one solution to TB and one solution to CPL gives us a solution to cLPI. The bicriteria guarantee of our algorithms allows us to control the solutions's trade-off between the returned size and the performance accuracy. New insights into the advantages of each solution are further discussed via experimental analysis.

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New technique for solving multivariate global optimization

Aaid,

Özer

2023

J. Numer. Anal. Approx. Theory

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In this paper, we propose an algorithm based on branch and bound method to underestimate the objective function and reductive transformation which is transformed the all multivariable functions on univariable functions. We also demonstrate several quadratic lower bound functions are proposed which they are better/preferable than the others well-known in literature. We obtain that our experimental results are more effective when we face different nonconvex functions.

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New technique for solving univariate global optimization

Cited by 3 publications

References 21 publications

Piecewise quadratic bounding functions for finding real roots of polynomials

Piecewise quadratic bounding functions for finding real roots of polynomials

Length-Bounded Paths Interdiction in Continuous Domain for Network Performance Assessment

New technique for solving multivariate global optimization

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