A hybrid method for solving non-convex min-max quadratic fractional problems under quadratic constraints

In this paper, we study a non-convex min-max fractional problem of quadratic functions subject to convex and non-convex quadratic constraints. First, by using the Dinkelbach-type method, we transform the fractional problem into a univariate nonlinear equation. To evaluate this equation, we need to s...

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Bibliographic Details
Published in:Optimization Vol. 71; no. 14; pp. 4107 - 4123
Main Authors: Osmanpour, Naser, Keyanpour, Mohammad
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 09.12.2022
Taylor & Francis LLC
Subjects:
Constraints
convex-concave procedure
Dinkelbach-type method
Iterative methods
Lower bounds
min-max fractional programming
non-convex constraint
Nonlinear equations
Quadratic equations
Quadratic programming
Upper bounds
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:In this paper, we study a non-convex min-max fractional problem of quadratic functions subject to convex and non-convex quadratic constraints. First, by using the Dinkelbach-type method, we transform the fractional problem into a univariate nonlinear equation. To evaluate this equation, we need to solve a non-convex quadratically constrained quadratic programming (QCQP) problem. To solve this problem, we propose a new method. In the proposed method, first, by using relaxation and convexification of non-convex constraints of non-convex QCQP problem, an upper bound and a lower bound of the optimal value is obtained. By using these bounds, we construct a parametric QCQP problem with two constraints. Then, by solution of the new problem, the parameters of this problem are updated for the next iteration. We show that the sequence of solutions of new problems is convergent to a global optimal solution of the non-convex QCQP problem. Numerical results are given to show the applicability of the proposed method.
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2021.1937158