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A Matlab toolbox for optimization over symmetric cones
TLDR
This paper describes how to work with SeDuMi, an add-on for MATLAB, which lets you solve optimization problems with linear, quadratic and semidefiniteness constraints by exploiting sparsity.
On Cones of Nonnegative Quadratic Functions
TLDR
It is shown that optimizing a general quadratic function over the intersection of an ellipsoid and a half-plane can be formulated as semidefinite programming (SDP), thus proving the polynomiality of this class of optimization problems, which arise, e.g., from the application of the trust region method for nonlinear programming.
Superlinear Convergence of a Symmetric Primal-Dual Path Following Algorithm for Semidefinite Programming
This paper establishes the superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming (SDP) under the assumptions that the semidefinite program has a
Error Bounds for Linear Matrix Inequalities
  • J. Sturm
  • Mathematics, Computer Science
    SIAM J. Optim.
  • 1 August 1999
TLDR
It is shown that for any bounded sequence of $\epsilon $-approximate solutions to a semidefinite programming problem, the distance to the optimal solution set is at most \( O(\epsil on ^{2^{-k}}) \), where k is the degree of singularity of the optimal solutions set.
Multivariate Nonnegative Quadratic Mappings
TLDR
This paper considers the set (cone) of nonnegative quadratic mappings, defined with respect to the positive semidefinite matrix cone, and study when it can be represented by linear matrix inequalities.
Implementation of interior point methods for mixed semidefinite and second order cone optimization problems
  • J. Sturm
  • Mathematics
    Optim. Methods Softw.
  • 1 January 2002
TLDR
This article is the first article to provide an elaborate discussion of the implementation of the primal-dual interior point method for mixed semidefinite and second order cone optimization in SeDuMi.
Linear matrix inequality formulation of spectral mask constraints with applications to FIR filter design
TLDR
A result is derived that allows us to precisely enforce piecewise constant and piecewise trigonometric polynomial masks in a finite and convex manner via linear matrix inequalities.
Conic convex programming and self-dual embedding
TLDR
The self-dual embedding technique proposed by Ye, Todd and Mizuno is extended to solve general conic convex programming, including semidefinite programmng and numerous examples from semideFinite programming are provided to illustrate various possibilities which have no analogue in the linear programming case.
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