Neurodynamic optimization model for bilevel programming with pseudoconvex upper-level optimization

Modern portfolio problems involve optimizing the risk-return trade-off, requiring simultaneous maximization of returns and minimization of risks, which often lead to a bilevel programming. Such optimization problems exhibit non-convex characteristics due to their hierarchical structure, which make it difficult for traditional optimization methods to obtain optimal solutions. This paper aims to construct a neurodynamic optimization model for solving a class of bilevel programming, in which the upper-level objective function is pseudoconvex and the lower level includes both equality and inequality constraints. First, by the Karush-Kuhn-Tucker (KKT) condition and projection theorems, the bilevel programming is transformed into a single-level programming, and the equivalence between the optimal solutions of these two problems is studied. Then, a neurodynamic optimization model with a comparator function and dynamic penalty parameters is designed. The state solution of the proposed model can converge to the feasible region of the optimization problem in finite time and further converge to an optimal solution of the considered problem. Finally, numerical examples are conducted to show the effectiveness of the model, and then an application in modern portfolio problem is provided.