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A Discussion on Non-Convex Optimization Problems Arising in Supply Chain Design and Finance

A Discussion on Non-Convex Optimization Problems Arising in Supply Chain Design and Finance

Arka Das
Copyright: © 2023 |Pages: 20
ISBN13: 9781668483862|ISBN10: 1668483866|ISBN13 Softcover: 9781668483879|EISBN13: 9781668483886
DOI: 10.4018/978-1-6684-8386-2.ch003
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MLA

Das, Arka. "A Discussion on Non-Convex Optimization Problems Arising in Supply Chain Design and Finance." Advancement in Business Analytics Tools for Higher Financial Performance, edited by Reza Gharoie Ahangar and Mark Napier, IGI Global, 2023, pp. 56-75. https://doi.org/10.4018/978-1-6684-8386-2.ch003

APA

Das, A. (2023). A Discussion on Non-Convex Optimization Problems Arising in Supply Chain Design and Finance. In R. Gharoie Ahangar & M. Napier (Eds.), Advancement in Business Analytics Tools for Higher Financial Performance (pp. 56-75). IGI Global. https://doi.org/10.4018/978-1-6684-8386-2.ch003

Chicago

Das, Arka. "A Discussion on Non-Convex Optimization Problems Arising in Supply Chain Design and Finance." In Advancement in Business Analytics Tools for Higher Financial Performance, edited by Reza Gharoie Ahangar and Mark Napier, 56-75. Hershey, PA: IGI Global, 2023. https://doi.org/10.4018/978-1-6684-8386-2.ch003

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Abstract

Non-convex optimization problems belong to a class of classical nonlinear optimization problems, which are often difficult to solve. An optimization problem becomes non-convex due to the presence of non-convex functions in the objective function or constraints. A function is a convex function if its Hessian matrix is positive and semi-definite for all values; otherwise, it is a non-convex function. A Hessian matrix is called positive semi-definite when the eigenvalues of the matrix are non-negative. A non-convex function can be either a concave function or a function that is neither a concave nor a convex function. A concave function is always negative semi-definite, indicating that the eigenvalues of the matrix are non-positive. This chapter starts with a short introduction to non-convex problems, followed by a discussion on different non-convex problems arising in supply chain and finance. Thereafter, the authors discuss different algorithms used for solving non-convex problems. Finally, the chapter conclude with the limitations of different algorithms.

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