Automatic Detection of Quasi-convexity of a Function for Estimation of the Range of its Values

Student: Dmitriev Ivan

Supervisor: Mikhail Posypkin

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Year of Graduation: 2024

Bounding of a function range is a key problem for global optimization, finding roots of equations and a number of other problems. The classical approach for solving this problem is interval analysis. In recent works, a method of improving this estimation by taking into account the convexity properties of the function has been proposed. Taking into account the quasi-convexity property of the function would further improve the obtained estimates. In this paper, we propose and implement an algorithm for automatically inferring the quasiconvexity of a function from its expression and taking this information into account to improve the estimates obtained by interval analysis.

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