arXiv subjects

Kaiping Liu

Publications and source records attributed to Kaiping Liu.

2 recordsLinked to original sources

arXiv2026

MPFA: A Pareto Front Approximation Method for Riemannian Bi-objective Optimization

We propose a Pareto front approximation (MPFA) method for smooth bi-objective optimization problems on Riemannian manifolds based on a Hermite interpolation technique. Compared with the existing multiobjective optimization numerical algorithms, the proposed method can generate a continuous approximate Pareto front without multiple initial points. We establish convergence of the proposed method and analyze the approximation error of the resulting Pareto front. Numerical experiments on several test problems demonstrate that the proposed approach can effectively approximate the Pareto front with high accuracy and reasonable computational cost. Furthermore, the method is applied to a bi-objective formulation of sparse principal component analysis, illustrating its practical applicability in data analysis problems.

math.OC↗

arXiv2024

A modified Polak-Ribiere-Polyak type conjugate gradient method with two stepsize strategies for vector optimization

In this paper, in order to find critical points of vector-valued functions with respect to the partial order induced by a closed, convex, and pointed cone with nonempty interior, we propose a nonlinear modified Polak-Ribiere-Polyak type conjugate gradient method with a nonnegative conjugate parameter. We show that the search direction in our method satisfies the sufficient descent condition independent of any line search. Furthermore, under mild assumptions, we obtain the results of global convergence with the standard Wolfe line search conditions as well as the standard Armijo line search strategy without convexity assumption of the objective functions. Computational experiments are given to show the effectiveness of the proposed method.

math.OC↗