Abstract
In this paper, we study a proximal-like algorithm for minimizing a closed proper function f(x) subject to x30, based on the iterative scheme: xk ε argmin{f(x) + μkd(x, xk-1)}, where d( , ) is an entropy-like distance function. The algorithm is well-defined under the assumption that the problem has a nonempty and bounded solution set. If, in addition, f is a differentiable quasi-convex function (or f is a differentiable function which is homogeneous with respect to a solution), we show that the sequence generated by the algorithm is convergent (or bounded), and furthermore, it converges to a solution of the problem (or every accumulation point is a solution of the problem) when the parameter μk approaches to zero. Preliminary numerical results are also reported, which further verify the theoretical results obtained.
Original language | English |
---|---|
Pages (from-to) | 319-333 |
Number of pages | 15 |
Journal | Pacific Journal of Optimization |
Volume | 4 |
Issue number | 2 |
Publication status | Published - 2008 May |
Keywords
- Entropy-like distance
- Homogeneous
- Proximal algorithm
- Quasi-convex
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Applied Mathematics