Abstract
Security issues are becoming more and more important to activities of individuals, organizations, and the society in our modern networked computerized world. In this chapter we survey a few optimization frameworks for problems related to security of various networked system such as the internet or the power grid system.
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Notes
- 1.
A function h of k variables is convex (resp. concave) if and only if, for all x 1, x 2, …, x k , y 1, y 2, …, y k and for all 0 < λ < 1, \(h\big((1-\lambda )\,\big(x_{1},x_{2},\ldots,x_{k}\big) +\lambda \,\big (y_{1},y_{2},\ldots,y_{k}\big)\big) \geq (1-\lambda )\,h\big(x_{1},x_{2},\ldots,x_{k}\big) +\lambda \, h\big(y_{1},y_{2},\ldots,y_{k}\big)\) (resp. \(h\big((1-\lambda )\,\big(x_{1},x_{2},\ldots,x_{k}\big) +\lambda \,\big (y_{1},y_{2},\ldots,y_{k}\big)\big) \leq (1-\lambda )\,h\big(x_{1},x_{2},\ldots,x_{k}\big) +\lambda \, h\big(y_{1},y_{2},\ldots,y_{k}\big)\,\)). When the objective function and all the constraints are convex (resp. concave), we have a convex (resp. concave) optimization problem. The convexity or concavity property often makes an optimization problem easier to solve as opposed to the general case; see [3] for further details.
- 2.
Okimoto et al. [18] claim that an advantage of finding all trade-off solutions is that agents can dynamically change decisions in case of emergencies. Unfortunately, the number of trade-off solutions may be exponential in the worst case.
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The authors were partially supported by NSF grant IIS-1160995.
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DasGupta, B., Srinivasan, V. (2017). A Review of Several Optimization Problems Related to Security in Networked System. In: Daras, N., Rassias, T. (eds) Operations Research, Engineering, and Cyber Security. Springer Optimization and Its Applications, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-319-51500-7_8
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