一类稀疏约束非线性规划的约束规格

研究一类带有闭凸集约束的稀疏约束非线性规划问题,这类问题在变量选择、模式识别、投资组合等领域具有广泛的应用.首先引进了限制性Slater约束规格的概念,证明了该约束规格强于限制性M-F约束规格,然后在此约束规格成立的条件下,分析了其局部最优解成立的充分和必要条件.最后,对约束集合的两种具体形式,指出限制性Slater约束规格必满足,并给出了一阶必要性条件的具体表达形式.

Constraint Qualifications for A Class of Sparse Nonlinear Programming

A class of sparse nonlinear programming was studied, whose feasible set is the intersection of a closed convex set and a sparse set. This model is a typical sparse optimization problem which has wide applications in variable selection, pattern recognition, portfolio management and other fields. We defined the restricted Slater constraint qualification for this sparse nonlinear programming and proved that this restricted Slater constraint qualification is stronger than the restricted M-F constraint qualification. Under this restricted Slater constraint qualification, we analyzed the necessary or sufficient optimality conditions for the local solutions. Finally, we provided the specific expressions of the first-order necessary optimality condition for the model with two specific constraint sets.