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- W4313407147 abstract "We consider necessary optimality conditions for optimization problems with equality constraints given in the operator form as $$F(x)=0$$ , where F is an operator between Banach spaces. The paper addresses the case when the Lagrange multiplier $$lambda _0$$ associated with the objective function might be equal to zero. If the equality constraints are not regular at some point $$x^*$$ in the sense that the Fréchet derivative of F at $$x^*$$ is not onto, then the point $$z^*=(x^*, lambda ^*_0, lambda ^*)$$ is a degenerate solution of the classical Lagrange system of optimality conditions $${mathcal {L}}(x, lambda _0, lambda )=0$$ , where $$x^*$$ is a solution of the optimization problem and $$(lambda ^*_0, lambda ^*)$$ is a corresponding generalized Lagrange multiplier. We derive new conditions that guarantee that $$z^*$$ is a locally unique solution of the Lagrange system. We also introduce a modified Lagrange system and prove that $$z^*$$ is its regular locally unique solution. The modified Lagrange system introduced in the paper can be used as a basis for constructing numerical methods for solving degenerate optimization problems. Our results are based on the construction of p–regularity and are illustrated by examples." @default.
- W4313407147 created "2023-01-06" @default.
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- W4313407147 date "2022-01-01" @default.
- W4313407147 modified "2023-09-26" @default.
- W4313407147 title "Degenerate Equality Constrained Optimization Problems and P-Regularity Theory" @default.
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- W4313407147 doi "https://doi.org/10.1007/978-3-031-22543-7_2" @default.
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