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- W1433227907 abstract "This paper considers a fractional programming problem (P) which minimizes a ratio of quadratic functions subject to a two-sided quadratic constraint. As is well-known, the fractional objective function can be replaced by a parametric family of quadratic functions, which makes (P) highly related to, but more difficult than a single quadratic programming problem subject to a similar constraint set. The task is to find the optimal parameter $lambda^*$ and then look for the optimal solution if $lambda^*$ is attained. Contrasted with the classical Dinkelbach method that iterates over the parameter, we propose a suitable constraint qualification under which a new version of the S-lemma with an equality can be proved so as to compute $lambda^*$ directly via an exact SDP relaxation. When the constraint set of (P) is degenerated to become an one-sided inequality, the same SDP approach can be applied to solve (P) {it without any condition}. We observe that the difference between a two-sided problem and an one-sided problem lies in the fact that the S-lemma with an equality does not have a natural Slater point to hold, which makes the former essentially more difficult than the latter. This work does not, either, assume the existence of a positive-definite linear combination of the quadratic terms (also known as the dual Slater condition, or a positive-definite matrix pencil), our result thus provides a novel extension to the so-called hard case of the generalized trust region subproblem subject to the upper and the lower level set of a quadratic function." @default.
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- W1433227907 date "2014-02-18" @default.
- W1433227907 modified "2023-09-27" @default.
- W1433227907 title "An SDP Approach For Solving Quadratic Fractional Programming Problems" @default.
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