On constraint qualifications for second-order optimality conditions depending on a single Lagrange multiplier |
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Institution: | 1. Department of Applied Mathematics, University of São Paulo, São Paulo, SP, Brazil;2. Department of Mathematics, Federal University of Paraná, Curitiba, PR, Brazil |
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Abstract: | We present new constraint qualifications (CQs) to ensure the validity of some well-known second-order optimality conditions. Our main interest is on second-order conditions that can be associated with numerical methods for solving constrained optimization problems. Such conditions depend on a single Lagrange multiplier, instead of the whole set of Lagrange multipliers. For each condition, we characterize the weakest CQ that guarantees its fulfillment at local minimizers, while proposing new weak conditions implying them. Relations with other CQs are discussed. |
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Keywords: | Nonlinear optimization Second-order optimality conditions Constraint qualifications |
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