Global Optimization of Functions of Several Variables Using Parallel Technologies

Grigoryev, I. V.; Мустафина, Светлана

doi:10.12732/ijpam.v106i1.24

Cited by 2 publications

(2 citation statements)

References 2 publications

(1 reference statement)

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“…We first consider a classic nonconvex optimization problem -the Styblinski-Tang function (STfunction) [15]. A 𝑑-dimensional ST-function is defined as…”

Section: Classic Nonconvex Test Functionmentioning

confidence: 99%

Can We Do Better Than Random Start? The Power of Data Outsourcing

Chen¹,

Dong²,

Tong³

2022

Preprint

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Many organizations have access to abundant data but lack the computational power to process the data. While they can outsource the computational task to other facilities, there are various constraints on the amount of data that can be shared. It is natural to ask what can data outsourcing accomplish under such constraints. We address this question from a machine learning perspective. When training a model with optimization algorithms, the quality of the results often relies heavily on the points where the algorithms are initialized. Random start is one of the most popular methods to tackle this issue, but it can be computationally expensive and not feasible for organizations lacking computing resources. Based on three different scenarios, we propose simulation-based algorithms that can utilize a small amount of outsourced data to find good initial points accordingly. Under suitable regularity conditions, we provide theoretical guarantees showing the algorithms can find good initial points with high probability. We also conduct numerical experiments to demonstrate that our algorithms perform significantly better than the random start approach.

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“…We first consider a classic nonconvex optimization problem -the Styblinski-Tang function (STfunction) [15]. A 𝑑-dimensional ST-function is defined as…”

Section: Classic Nonconvex Test Functionmentioning

confidence: 99%

Can We Do Better Than Random Start? The Power of Data Outsourcing

Chen¹,

Dong²,

Tong³

2022

Preprint

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“…The decision of system (1) in the conditions of (2) can be received by various numerical methods of the Cauchy problem interval solution [3]. In [4] the algorithm of the combined method of the sensitivity interval analysis adapted for the solution of chemical kinetics problems is described.…”

Section: Introductionmentioning

confidence: 99%

The Method of Research of the Direct Problem to the Variation of the Kinetic Parameters Within a Given Range

Mustafina¹,

Vaytiev²,

Grigoryev³

2017

Int. J. of Pure and Appl. Math.

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The paper shows a technique of researching of the direct kinetic problem sensitivity to the variation of the kinetic parameters within a given range. This technique is based on use of the computing device of the interval analysis. The direct problem solution in the conditions of kinetic parameters uncertainty was received by the interval method of the solution of a Cauchy problem for differential equations system. This interval method was adapted to the problems of chemical kinetics. The interval characteristics received during this method application were used for research of reagents and products concentration sensitivity in relation to kinetic parameters of mathematical model of industrially important reaction.

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Global Optimization of Functions of Several Variables Using Parallel Technologies

Cited by 2 publications

References 2 publications

Can We Do Better Than Random Start? The Power of Data Outsourcing

Can We Do Better Than Random Start? The Power of Data Outsourcing

The Method of Research of the Direct Problem to the Variation of the Kinetic Parameters Within a Given Range

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