### Abstract

In this paper, we study a proximal-like algorithm for minimizing a closed proper function f(x) subject to x^{3}0, based on the iterative scheme: x^{k} ε argmin{f(x) + μkd(x, x^{k-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 μ^{k} approaches to zero. Preliminary numerical results are also reported, which further verify the theoretical results obtained.

Original language | English |
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Pages (from-to) | 319-333 |

Number of pages | 15 |

Journal | Pacific Journal of Optimization |

Volume | 4 |

Issue number | 2 |

Publication status | Published - 2008 May 1 |

### Keywords

- Entropy-like distance
- Homogeneous
- Proximal algorithm
- Quasi-convex

### ASJC Scopus subject areas

- Control and Optimization
- Computational Mathematics
- Applied Mathematics

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## Cite this

*Pacific Journal of Optimization*,

*4*(2), 319-333.