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تسجيل مستخدم جديدBilevel Polynomial Programs and Semidefinite Relaxation Methods
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A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as semi-infinite polynomial programs (SIPPs), using Fritz John conditions and Jacobian representations. Combining the exchange technique and Lasserre type semidefinite relaxations, we propose numerical methods for solving both simple and general BPPs. For simple BPPs, we prove the convergence to global optimal solutions. Numerical experiments are presented to show the efficiency of proposed algorithms.
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The bilevel program is an optimization problem where the constraint involves solutions to a parametric optimization problem. It is well-known that the value function reformulation provides an equivalent single-level optimization problem but it result
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