# A class of customized proximal point algorithms for linearly constrained convex optimization

## Abstract

In this paper, we propose a class of customized proximal point algorithms for linearly constrained convex optimization problems. The algorithms are implementable, provided that the proximal operator of the objective function is easy to evaluate. We show that, with special setting of the algorithmic scalar, our algorithms contain the customized proximal point algorithm (He et al., Optim Appl 56:559–572, 2013), the linearized augmented Lagrangian method (Yang and Yuan, Math Comput 82:301–329, 2013), the Bregman Operator Splitting algorithm (Zhang et al., SIAM J Imaging Sci 3:253–276, 2010) as special cases. The global convergence and worst-case convergence rate measured by the iteration complexity are established for the proposed algorithms. Numerical results demonstrate that the algorithms work well for a wide range of the scalar.

- Authors:

- High-Tech Institute of Xi’an (China)
- PLA University of Science and Technology, College of Communications Engineering (China)

- Publication Date:

- OSTI Identifier:
- 22769365

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; CONVERGENCE; LAGRANGIAN FUNCTION; LIMITING VALUES; OPTIMIZATION; SCALARS

### Citation Formats

```
Ma, Feng, and Ni, Mingfang.
```*A class of customized proximal point algorithms for linearly constrained convex optimization*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0371-3.

```
Ma, Feng, & Ni, Mingfang.
```*A class of customized proximal point algorithms for linearly constrained convex optimization*. United States. doi:10.1007/S40314-016-0371-3.

```
Ma, Feng, and Ni, Mingfang. Tue .
"A class of customized proximal point algorithms for linearly constrained convex optimization". United States. doi:10.1007/S40314-016-0371-3.
```

```
@article{osti_22769365,
```

title = {A class of customized proximal point algorithms for linearly constrained convex optimization},

author = {Ma, Feng and Ni, Mingfang},

abstractNote = {In this paper, we propose a class of customized proximal point algorithms for linearly constrained convex optimization problems. The algorithms are implementable, provided that the proximal operator of the objective function is easy to evaluate. We show that, with special setting of the algorithmic scalar, our algorithms contain the customized proximal point algorithm (He et al., Optim Appl 56:559–572, 2013), the linearized augmented Lagrangian method (Yang and Yuan, Math Comput 82:301–329, 2013), the Bregman Operator Splitting algorithm (Zhang et al., SIAM J Imaging Sci 3:253–276, 2010) as special cases. The global convergence and worst-case convergence rate measured by the iteration complexity are established for the proposed algorithms. Numerical results demonstrate that the algorithms work well for a wide range of the scalar.},

doi = {10.1007/S40314-016-0371-3},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}