On SOCP/SDP formulation of the extended trust region subproblem
S. Fallahi, M. Salahi, S. Ansary Karbasy
TL;DR
This paper addresses the extended trust region subproblem by deriving optimality conditions and formulating it as an SOCP/SDP, providing a new approach for solving indefinite quadratic minimization with constraints.
Contribution
It introduces a novel SOCP/SDP formulation for the extended trust region subproblem and establishes necessary and sufficient optimality conditions using a variation of the S-Lemma.
Findings
Derived necessary and sufficient optimality conditions for TRS
Proposed an SOCP/SDP formulation for TRS
Provided illustrative examples demonstrating the approach
Abstract
In this paper, we consider the extended trust region subproblem (\eTRS) which is the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of S-Lemma, we derive the necessary and sufficient optimality conditions for \eTRS. Then an SOCP/SDP formulation is introduced for the problem. Finally, several illustrative examples are provided.
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Taxonomy
TopicsSecurity in Wireless Sensor Networks · Cloud Computing and Resource Management · Cryptography and Data Security