Multi objective programming problems have been widely applied to various engineering areas which include optimal design of an automotive engine, economics, and military strategies. In this paper, we propose a noninterior path following algorithm to solve a class of multi objective programming problems. Under suitable conditions, a smooth path will be proven to exist. This can give a constructive proof of the existence of solutions and lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper. [ABSTRACT FROM AUTHOR]
Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the l₁-norm minimization problem (2011). The advantage of this method is its simplicity and lower storage. In this paper, based on new nonsmooth equations reformulation, we investigate new nonsmooth equations-based algorithms for solving l₁-norm minimization problems. Under mild conditions, we show that the proposed algorithms are globally convergent. The preliminary numerical results demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]