Complex and quaternionic optimization

Yuly Shipilevsky

doi:10.3934/naco.2019051

Article Contents

2020, Volume 10, Issue 3: 249-255. Doi: 10.3934/naco.2019051

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Complex and quaternionic optimization

Yuly Shipilevsky

507-111 Ridelle Avenue, Toronto, Ontario, M6B 1J7, Canada

Received: February 2019

Revised: October 2019

Published online: February 5, 2020

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Abstract

We introduce and suggest to research a special class of optimization problems, wherein an objective function is a real-valued complex variables function under constraints, comprising complex-valued complex variables functions: "Complex Optimization". We demonstrate multiple examples to show a rich variety of problems, describing Complex Optimization as an optimization subclass as well as a Mixed Integer-Real-Complex Optimization.

Next, we introduce more general concept: "Quaternionic Optimization" for optimization over quaternion subsets.

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Mathematics Subject Classification: Primary: 90C48; Secondary: 30D30, 30A99.

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