Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 4,852 papers for “Semidefinite programming”

Semidefinite programming

Paul Skrzypczyk, Daniel Cavalcanti · 2023

In this chapter we cover the fundamental aspects of semidefinite programming, which will be seen to be closely related to the fundamental aspects of linear programming covered in the previous chapter. Whereas in the context of linear programming the basic objects of interest were real vectors, in the context of semidefinite programming, the basic objects of interest are Hermitian operators. We will see later in this chapter that linear programming can in fact be viewed as a special instance of semidefinite programming, which also explains why the two are so intimately related to each other.

Cited by 0

Semidefinite Programming

Ding‐Zhu Du, Pãnos M. Pardalos, Weili Wu · Nonconvex optimization and its applications · 2001

Cited by 9

Semidefinite Programming

2017

In semidefinite programming, one minimizes a linear function subject to the constraint that an affine combination of symmetric matrices is positive semidefinite.Such a constraint is nonlinear and nonsmooth, but convex, so semidefinite programs are convex optimization problems.Semidefinite programming unifies several standard problems (e.g., linear and quadratic programming) and finds many applications in engineering and combinatorial optimization.Although semidefinite programs are much more general than linear programs, they are not much harder to solve.Most interior-point methods for linear programming have been generalized to semidefinite programs.As in linear programming, these methods have polynomial worst-case complexity and perform very well in practice.This paper gives a survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution.

Cited by 4

Semidefinite Programming

Cristóbal Guzmán, Lovász Theta Function · 2013

• SDP gives best relaxations known for some combinatorial optimization problems. • Medium/large scale SDP are beyond the grasp of computational tractability (although polynomial). • Many combinatorial applications are invariant under a group action. • These symmetries lead to nice block decompositions of the SDP, making them computationally tractable. 3 / 74 Objectives • Show the modeling capabilities of SDP. • Show through examples how to exploit symmetries for simplifying SDP formulations. • Generalize SDP models to infinite dimensions, through combinatorial applications. 4 / 74

Cited by 0

Semidefinite Programming

Ding‐Zhu Du, Ker‐I Ko, Xiao Hu · Springer optimization and its applications · 2011

Cited by 4

Scalable Semidefinite Programming

Alp Yurtsever, Joel A. Tropp, Olivier Fercoq et al. · SIAM Journal on Mathematics of Data Science · 2021

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP problems by economizing on the storage and arithmetic costs. Numerical evidence shows that the method is effective for a range of applications, including relaxations of \sf MaxCut, abstract phase retrieval, and quadratic assignment. Running on a laptop equivalent, the algorithm can handle SDP instances where the matrix variable has over $10^{14}$ entries.

Cited by 77Open access

SEMIDEFINITE QUASICONCAVE PROGRAMMING

Rentsen Enkhbat, T. Bayartugs · International Journal of Pure and Apllied Mathematics · 2013

We introduce so-called semidefinite quasiconcave programming or equivalently semidefinite quasiconvex maximization problem. We derive new global optimality conditions by generalizing Based on the global optimality conditions, we construct an algorithm which generates a sequence of local maximizers that converges to a global solution. Subproblems of the proposed algorithm are semidefinite linear programming.

Cited by 0Open access

Online Semidefinite Programming

Noa Elad, Satyen Kale, Joseph Naor · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2016

We consider semidefinite programming through the lens of online algorithms - what happens if not all input is given at once, but rather iteratively? In what way does it make sense for a semidefinite program to be revealed? We answer these questions by defining a model for online semidefinite programming. This model can be viewed as a generalization of online coveringpacking linear programs, and it also captures interesting problems from quantum information theory. We design an online algorithm for semidefinite programming, utilizing the online primaldual method, achieving a competitive ratio of O(log(n)), where n is the number of matrices in the primal semidefinite program. We also design an algorithm for semidefinite programming with box constraints, achieving a competitive ratio of O(log F*), where F* is a sparsity measure of the semidefinite program. We conclude with an online randomized rounding procedure.

Cited by 0Open access

Robust Semidefinite Programming

Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski · 2010

In this paper, we consider semidefinite programs where the data is only known to belong to some uncertainty set U. Following recent work by the authors, we develop the notion of robust solution to such problems, which are required to satisfy the (uncertain) constraints whatever the value of the data in U. Even when the decision variable is fixed, checking robust feasibility is in general NP-hard. For a number of uncertainty sets U, we show how to compute robust solutions, based on a sufficient condition for robust feasibility, via SDP. We detail some cases when the sufficient condition is also necessary, such as linear programming or convex quadratic programming with ellipsoidal uncertainty. Finally, we provide examples, taken from interval computations and truss topology design.

Cited by 0

Semidefinite Programming and Integer Programming

Monique Laurent, Franz Rendl, Aardal, Karen et al. · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2003

We survey how semidefinite programming can be used for finding good approximative solutions to hard combinatorial optimization problems.

Cited by 1Open access

Semidefinite Programming and Constraint Programming

Willem-Jan Hoeve · RePEc: Research Papers in Economics

Abstract Recently, semidefinite programming relaxations have been applied in constraint programming to take advantage of the high-quality bounds and precise heuristic guidance during the search for a solution. The purpose of this chapter is to present an overview of these developments, and to provide future research prospects.

Cited by 0

Semidefinite Programming Applied to Nonlinear Programming

Serge G. Kruk, U. Von Matt W. G, G. Golub et al. · 1997

ces, Rice University, Houston, TX, 1990. [74] R.B. Wilson. A simplicial algorithm for concave programming. PhD thesis, Harvard University, 1963. [75] Y. Yuan. On a subproblem of trust region algorithms for constrained optimization. Mathematical Programming, 47:53--63, 1990. [76] Y. Yuan. A dual algorithm for minimizing a quadratic function with two quadratic constraints. Journal of Computational Mathematics, 9:348--359, 1991. BIBLIOGRAPHY 95 [55] M.J.D. Powell and Y. Yuan. A trust region algorithm for equality constrained optimization. Technical Report DAMTP 1986/NA2, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England, 1986. [56] F. Rendl. A matlab toolbox for semidefinite programming. Technical report, Technische Universitat Graz, Graz, Austria, 1994. [57] F. Rendl and H. Wolkowicz. A semidefinite framework for trust region subproblems with applications to large scal

Cited by 0

1 SemiDefinite Programming and Two Applications 1.1 Overview of SemiDefinite Programming

2008

This lecture started with the semidefinite programming and its applications in two areas: the side-chain positioning problem and the sensor network localization problem. Next, we presented the distance geometry with orientation constraints: we first introduced the graph embedding problem with the angle information and then presented the protein backbone determination using the global orientational constraints from RDC data.

Cited by 0