For approximation analysis of multiobjective optimization problems,we will introduce vector variational principles for vector-valued functions and some equivalence among the vector variational principles and some important theorems in nonlinear analysis.

In this paper,we give a vectorial Ekeland variational principle with a w-distance,a vectorial Takahashi nonconvex minimization theorem with a w-distance and a vectorial Caristi fixed point theorem with a w-distance.

Analytical solutions of composite modulus of multi-element composite foundation by parametric variational principle;

The analytical solutions of composite modulus in both elastic and plastic conditions are deduced by applying parametric variational principle.

Based on Perzyna visco_plasticity model and parametric variational principle,the full coupled variational principle and its F.

This paper proposed the elastoplastic constitutive model of swelling rock based on the humidity stress field theory and by using parametric variation principle to establis.

Based on updated Lagrangian formulation of elasto-plastic large deformation theory,the numerical simulation method of Biot′s consolidation theory on elasto-plastic large deformation is developed using the idea of parametric variation principle.

Numerical manifold method of elastoplastic analysis is presented by using the parametric variation principle.

Based on energy variation principle,the governing differential equations and the corresponding boundary conditions of box girder with consideration for the shear lag effect and shear deformation as well as rotational inertia were induced.

The energy variation principle is applied to establish the governing differential equations and corresponding natural boundary conditions on the static and dynamic characteristics of thin-walled I-beam, and closed-form solutions of generalized displacements are obtained.