混合约束多目标优化问题的凝聚同伦内点方法

考虑用凝聚同伦内点法求解带有等式和不等式约束的凸多目标优化问题,先用凝聚函数法将目标函数和约束条件进行光滑逼近,再用组合同伦方法证明可行域内任一点在广义弱法锥条件下几乎处处收敛于混合多目标问题的弱有效解.数值计算结果表明,所给方法有效、可行.

Aggregate Homotopy Interior Point Method forMultiobjective Programming Problem withEquality and Inequality Constraints

The aggregate homotopy interior point method was used to solve the convex multiobjective programming problem with mixed equality and inequality constraints. The objective functions and contraints were smoothed with aggregate functions. A path tracing algorithm was adopted to find its weak effective solutions, which was proved by homotopy method. Numerical examples demonstrated the effectivness and feasibility of this method.