## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

The aim of this paper is to develop second-order necessary and second-order sufficient optimality conditions for cone constrained multi-objective optimization. First of all, we derive, for an abstract constrained multi-objective optimization problem, two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions. Secondly, basing on the optimality results for the abstract problem, we demonstrate, for cone constrained multi-objective optimization problems, the first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as the second-order sufficient optimality conditions under upper second-order regularity for the conic constraint. Finally, using the optimality conditions for cone constrained multi-objective optimization obtained, we establish optimality conditions for polyhedral cone, second-order cone and semi-definite cone constrained multi-objective optimization problems.

This paper focuses on a class of mathematical programs with symmetric cone complementarity constraints (SCMPCC). The explicit expression of C-stationary condition and SCMPCC-linear independence constraint qualification (denoted by SCMPCC-LICQ) for SCMPCC are first presented. We analyze a parametric smoothing approach for solving this program in which SCMPCC is replaced by a smoothing problem $P_{\varepsilon}$ depending on a (small) parameter $\varepsilon$. We are interested in the convergence behavior of the feasible set, stationary points, solution mapping and optimal value function of problem $P_{\varepsilon}$ when $\varepsilon \to 0$ under SCMPCC-LICQ. In particular, it is shown that the convergence rate of Hausdorff distance between feasible sets $\mathcal{F}_{\varepsilon}$ and $\mathcal{F}$ is of order $\mbox{O}(|\varepsilon|)$ and the solution mapping and optimal value of $P_{\varepsilon}$ are outer semicontinuous and locally Lipschitz continuous at $\varepsilon=0$ respectively. Moreover, any accumulation point of stationary points of $P_{\varepsilon}$ is a C-stationary point of SCMPCC under SCMPCC-LICQ.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]