| J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones." Optimization methods and software, vol. 11-12, no. 1-4, pp. 625--653, 1999, version 1.1 available from http://sedumi.mcmaster.ca/. |
....method and could probably handle larger sparse cases nearly as well as MOSEK. LOQO finally, is a general NLP code and it treats the SOCP problems as smoothed nondi#erentiable NLPs which in some cases leads to larger iteration counts. 22 Table 2: Comparison of our methods with the codes [1, 12, 14, 15] A. 4.4 A. 4.5 A.4.2 SeDu SDPT MOSK LOQO EX1 50 13 15 20 13 12 13 44 EX1 75 16 14 21 16 11 13 44 EX1 100 14 16 22 16 12 14 51 EX1 200 17 17 23 16 12 16 60 EX2 50 9 10 13 15 9 8 13 EX2 100 8 13 13 12 10 8 14 EX2 150 9 9 14 15 10 10 12 EX2 200 10 9 14 14 10 10 13 EX3 10 4 13 14 18 13 21 10 88 ....
Jos F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimization Methods and Software, 11/12 (1999), pp. 625--653.
....H(P ) 0: Proof: It is an application of the projection lemma, an algebraic result well known to the control community, see e.g. Skelton, 1998, Theorem 2.3.12] 2 4 Application to Robust Stability Analysis In all the following numerical examples we solved the LMI problems with SeDuMi 1. 04 [Sturm, 1999] running under Matlab 6.1 on a Sun Sparc Workstation Ultra 5. We notice that the LMI condition of Lemma 5 is simultaneously linear in coefficients of N(s) and in Lyapunov matrix P . This property can be exploited to provide less conservative convex conditions than the well known quadratic ....
J. F. Sturm "Using SeDuMi 1.02, a Matlab Toolbox for Optimization over Symmetric Cones", Optimization Methods and Software, Vol. 11-12, pp. 625--653, 1999. See also fewcal.kub.nl/sturm. 14
....convex constraints on the controller coefficients can freely be incorporated, such as spectral or interpolation constraints on the controller dynamics. The simplicity and efficiency of the approach is illustrated on several numerical examples found in the literature, and a basic Matlab 1 SeDuMi [Sturm, 1999] implementation of the robust SPR design algorithm is given in the Appendix. A more sophisticated version of the design algorithm will be implemented into the next release 3.0 of the Polynomial Toolbox for Matlab [Polyx Ltd. 2001] 1 Matlab is a trademark of The MathWorks, Inc. 2 2 Main ....
.... frequently in control and signal processing [Vandenberghe, 1996] but also in convex relaxations to combinatorial optimization problems [Lasserre, 2001] Several user friendly packages have been developed to solve this convex optimization problem, such as the freeware SeDuMi interfaced with Matlab [Sturm, 1999]. In the next section, we show how robust SPR design problems can be solved in a matter of seconds with the help of this software. Before doing this, we will show that our approach is also suitable for solving the related problem of strengthened SPR design [Anderson, 1994] Corollary 1 Under the ....
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J. F. Sturm "Using SeDuMi 1.02, a Matlab Toolbox for Optimization over Symmetric Cones", Optimization Methods and Software, Vol. 11-12, pp. 625--653, 1999. See also fewcal.kub.nl/sturm.
....closely approximates F W . Replacing F W by such a set, the optimization problem becomes convex and therefore tractable [22] Moreover, if this set is described by linear inequalities, the convex relaxed problem becomes an SDP [32] and hence, efficiently solvable by currently available software [4, 9, 26, 28]. Goh et al. 14] proposed the (convex) polytope f G W to approximate F W : f G W = x ; y ; W ) 2 IR n 2 IR m 2 IR n2m : x ; y) 2 H; w ij w ij w ij ; i 2 I n ; j 2 J m ) where w ij = minfx i y j ; x i y j ; x i y j ; x i y j g w ij = maxfx i y j ; x i y j ; x i y j ; ....
....The convex relaxations and the algorithms exposed here can be naturally extended to optimization problems with a bilinear objective function and BMI constraints. On the contrary of the BMIEPs which are always feasible, these problems can be infeasible. However, the currently available SDP packages [9, 26, 28] can detect infeasibility of the SDPs, and therefore, only minor modifications are necessary in the proposed algorithms to solve these problems. A different approach to solve problems involving BMIs was recently proposed by Kojima and Tun cel. They announced two conceptual algorithms based on LP ....
J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Department of Quantitative Economics, Maastricht University, Maastricht, The Netherlands, August 1998. Available at http://www.unimaas.nl/~sturm/software/sedumi.html.
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J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones." Optimization methods and software, vol. 11-12, no. 1-4, pp. 625--653, 1999, version 1.1 available from http://sedumi.mcmaster.ca/.
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J. S. Sturm, "Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones," Tech. Rep., Tilburg University, Department of Econometrics, Netherlands, 2001, http://fewcal.kub.nl/ sturm.
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F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimization Methods and Software, 11-12 (1999), pp. 625-653, Special issue on Interior Point Methods (CD supplement with software).
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J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optim. Methods and Softw. 11--12 (1999) 625--653. Available at http://fewcal.kub.nl/sturm/software/sedumi.html.
No context found.
F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimization Methods and Software, 11-12 (1999) 625-653. Special issue on Interior Point Methods (CD supplement with software).
No context found.
J. Sturm, "Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones," Optimization Methods and Software, vol. 11-12, pp. 625--653, 1999.
No context found.
J. Sturm, "Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones," Optimization Methods and Software, vol. 11-12, pp. 625--653, 1999.
No context found.
J. Sturm, "Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones," Optimization Methods and Software, vol. 11-12, pp. 625--653, 1999.
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J. S. Sturm, "Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones," Tech. Rep., Tilburg To obtain this plot, we have used the adaptive grid refinement approach from Section 5 to get point estimates not limited to the grid.
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J. F. Sturm, "Using SEDUMI 1.02, a Matlab toolbox for optimizations over symmetric cones," Optimization Meth. and Soft., vol. 11-12, 1999.
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J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optim. Meth. Software, vol. 11--12, pp. 625--653, 1999. Also: http://www. unimaas.nl/sturm/software/sedumi.html.
No context found.
J. F. Sturm, "Using SEDUMI 1.02, a Matlab toolbox for optimizations over symmetric cones," Optimization Meth. and Soft., vol. 11-12, 1999.
No context found.
J.F. STURM, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones", Optimization Methods and Software, vol. 11-12, 1999, pages 625-653, URL: fewcal.kub.nl /sturm/software/sedumi.html.
No context found.
J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optim. Methods and Softw. 11--12 (1999) 625--653. Available at http://fewcal.kub.nl/sturm/software/sedumi.html.
No context found.
J. F. Sturm, "Using SeDuMi 1.02, MATLAB toolbox for optimization over symmetric cones," Optim. Methods and Software 11--12 (1999) 625--653.
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