最小约束违背非线性凸优化

Nonlinear Convex Optimization with Least Constraint Violation

摘要: 本文基于不可行性度量和互补约束优化模型的角度研究最小约束违背凸优化问题。首先我们对约束不相容的凸优化问题建立了最小约束违背优化模型。当问题中的约束相容时，该模型可退化为原始问题。当约束不相容时，该模型等价于某个MPCC问题。其次我们证明了该等价问题的W-稳定性。最后我们用增广拉格朗日方法求解该等价问题，证明了该方法生成的点列收敛到等价MPCC问题的W-稳定点。

Abstract: In this paper, the problem of least constrained contracorvex optimization is studied from the perspective of the infeasibility measure and the complementary constraint optimization model. Firstly, we establish a minimum constraint violation optimization model for the convex optimization problem with incompatible constraints. When the constraints in the problem are compatible, the model can degenerate to the original problem. When the constraints are incompatible, the model is equivalent to an MPCC problem. Second, we demonstrate the W-stability of the equivalence problem. Finally, we use the augmented Lagrangian method to solve the equivalence problem, and prove that the point series generated by the method converges to the W-stable point of the equivalent MPCC problem.