Random projections for conic programs

Leo Liberti; Pierre Louis Poirion; Ky Vu

doi:10.1016/j.laa.2021.06.010

Random projections for conic programs

Leo Liberti
, Pierre Louis Poirion
, Ky Vu

RIKEN AIP
FPT University

Research output: Contribution to journal › Article › peer-review

Abstract

We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan algebras. We then discuss some computational experiments on randomly generated semidefinite programs in order to illustrate the practical applicability of our ideas.

Original language	English
Pages (from-to)	204-220
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	626
DOIs	https://doi.org/10.1016/j.laa.2021.06.010
Publication status	Published - 1 Oct 2021

Keywords

Approximation
Johnson-Lindenstrauss lemma
Jordan algebra
Mathematical programming

Access to Document

10.1016/j.laa.2021.06.010

Cite this

@article{1dfe928a22094223ac7e898ab8bea1c9,

title = "Random projections for conic programs",

abstract = "We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan algebras. We then discuss some computational experiments on randomly generated semidefinite programs in order to illustrate the practical applicability of our ideas.",

keywords = "Approximation, Johnson-Lindenstrauss lemma, Jordan algebra, Mathematical programming",

author = "Leo Liberti and Poirion, \{Pierre Louis\} and Ky Vu",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = oct,

day = "1",

doi = "10.1016/j.laa.2021.06.010",

language = "English",

volume = "626",

pages = "204--220",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

}

TY - JOUR

T1 - Random projections for conic programs

AU - Liberti, Leo

AU - Poirion, Pierre Louis

AU - Vu, Ky

PY - 2021/10/1

Y1 - 2021/10/1

N2 - We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan algebras. We then discuss some computational experiments on randomly generated semidefinite programs in order to illustrate the practical applicability of our ideas.

AB - We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan algebras. We then discuss some computational experiments on randomly generated semidefinite programs in order to illustrate the practical applicability of our ideas.

KW - Approximation

KW - Johnson-Lindenstrauss lemma

KW - Jordan algebra

KW - Mathematical programming

UR - https://www.scopus.com/pages/publications/85108334708

U2 - 10.1016/j.laa.2021.06.010

DO - 10.1016/j.laa.2021.06.010

M3 - Article

AN - SCOPUS:85108334708

SN - 0024-3795

VL - 626

SP - 204

EP - 220

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Random projections for conic programs

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this