# On OM-decomposable sets

## Abstract

We introduce and study the family of sets in a finite-dimensional Euclidean space which can be written as the Minkowski sum of an open, bounded, and convex set and a closed convex cone. We establish several properties of the class of such sets, called OM-decomposable, some of which extend related properties holding for the class of Motzkin decomposable sets (i.e., those for which the convex and bounded set in the decomposition is requested to be closed, hence compact).

- Authors:

- Estrada Dona Castorina 110, Instituto de Matématica Pura e Aplicada (IMPA) (Brazil)
- Universidad de las Américas, Department of Actuary and Mathematics (Mexico)

- Publication Date:

- OSTI Identifier:
- 22771097

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 3; 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; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONES; EUCLIDEAN SPACE; FINITE ELEMENT METHOD; HILBERT SPACE; MINKOWSKI SPACE

### Citation Formats

```
Iusem, A. N., E-mail: iusp@impa.br, and Todorov, M. I.
```*On OM-decomposable sets*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3758-4.

```
Iusem, A. N., E-mail: iusp@impa.br, & Todorov, M. I.
```*On OM-decomposable sets*. United States. doi:10.1007/S10958-018-3758-4.

```
Iusem, A. N., E-mail: iusp@impa.br, and Todorov, M. I. Sun .
"On OM-decomposable sets". United States. doi:10.1007/S10958-018-3758-4.
```

```
@article{osti_22771097,
```

title = {On OM-decomposable sets},

author = {Iusem, A. N., E-mail: iusp@impa.br and Todorov, M. I.},

abstractNote = {We introduce and study the family of sets in a finite-dimensional Euclidean space which can be written as the Minkowski sum of an open, bounded, and convex set and a closed convex cone. We establish several properties of the class of such sets, called OM-decomposable, some of which extend related properties holding for the class of Motzkin decomposable sets (i.e., those for which the convex and bounded set in the decomposition is requested to be closed, hence compact).},

doi = {10.1007/S10958-018-3758-4},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 3,

volume = 37,

place = {United States},

year = {2018},

month = {7}

}

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