Reduction and Linearisation of Quadratic Constrained Optimisation in Linked Systems

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Abstract
A new method is presented for reducing and solving by linear methods a class of quadratic constrained optimisation problems. The type of problem occurs in interconnected physical systems and situations characterised by the sum of quadratic functions linked successively in pairs by common variables. Transformations produce a new objective function of only the terminal variables when the objective function is stationary with respect to the linking variables. This reduced objective function is optimised with most original constraints absorbed in the transformations themselves and those remaining form a single matrix constraint, also in the terminal variables, allowing application of undetermined multipliers to formulate an eigenvalue problem, the eigenvector solution of which allows the use of standard linear techniques from there onwards. Two different types of example are given: optimising data flow in computer networks and a new method for the design of broadband multilayer absorbers with specified included layer(s).

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