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Approximating Pareto curves using semidefinite relaxations. (English) Zbl 1408.90273

Summary: We approximate as closely as desired the Pareto curve associated with bicriteria polynomial optimization problems. We use three formulations (including the weighted sum approach and the Chebyshev approximation) and each of them is viewed as a parametric polynomial optimization problem. For each case is associated a hierarchy of semidefinite relaxations and from an optimal solution of each relaxation one approximates the Pareto curve by solving an inverse problem (first two cases) or by building a polynomial underestimator (third case).

MSC:

90C29 Multi-objective and goal programming
90C22 Semidefinite programming
90C31 Sensitivity, stability, parametric optimization
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