Computation of the distance to semi-algebraic sets
ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 139-156. 
@article{COCV_2000__5__139_0,
     author = {Ferrier, Christophe},
     title = {Computation of the distance to semi-algebraic sets},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {139--156},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2000},
     mrnumber = {1744609},
     zbl = {1054.14534},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2000__5__139_0/}
}
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Ferrier, Christophe. Computation of the distance to semi-algebraic sets. ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 139-156. http://www.numdam.org/item/COCV_2000__5__139_0/

[1] F. Alizadeth, Interior point methods in semidefinite programming with application to combinatorial optimisation. SIAM J. Optim. 5 ( 1995) 13-51. | MR | Zbl

[2] A. Bellido, Construction de fonctions d'itération pour le calcul simultané des solutions d'équations et de systèmes d'équations algébriques. Thèse de doctorat de l'Universté Paul Sabatier, Toulouse ( 1992).

[3] S. Boydet al., Linear Matrix Inequalities Problem in Control Theory. SIAM, Philadelphia, Stud. Appl. Math. 15 ( 1995).

[4] J.-P. Dedieu and J.-C. Yakoubsohn, Localization of an algebraic hypersurface by the exclusion algorithm. Comm. Comput. 2 ( 1992) 239-256. | MR | Zbl

[5] Ch. Ferrier, Hubert's 17th problem and best dual bounds in quadratic minimization. Cybernetics and System Analysis 5 ( 1998) 76-91. | MR | Zbl

[6] A.V. Fiacco and G.P. Mccormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques. John Wiley ( 1968). Reprinted SIAM, 1990. | MR | Zbl

[7] R. Fletcher, Semi-defmite matrix constraints in optimization. SIAM J. Control Optim. 23 ( 1985) 493-513. | MR | Zbl

[8] C. Lemarechal and J.-B. Hiriart-Urruty, Convex Analysis and Minimization Algorithms II. Springer Verlag, Comprehensive Studies in Mathematics 306 ( 1991). | MR | Zbl

[9] F. Jarre, Interior-point methods for convex programming. Appl. Math. Optim. 26 ( 1992) 287-391. | MR | Zbl

[10] F. Jarre, An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices. SIAM J. Control Optim. 31 ( 1993) 1360-1377. | MR | Zbl

[11] N. Karmarkar, A new polynomial-time algorithm for linear programming. Combinatorica 4 ( 1984) 373-395. | MR | Zbl

[12] R.B. Kearfott, Some tests of generalized bisection. ACM Trans. Math. Software 13 ( 1987197-200. | MR | Zbl

[13] Yu. Nesterov and A. Nemirovsky, Interior-point polynomial methods in convex programming. SIAM, Philadelphia, Stud. Appl. Math. 13 ( 1994). | Zbl

[14] N.Z. Shor, Dual estimate in multi-extremal problems. J. Global Optim. 2 ( 1992) 411-418. | Zbl

[15] G. Sonnevend, An "analytical centre" for polyhedrons and a new classe of global algorithms for linear (smooth, convex) programming. Springer Verlag, Lecture Notes in Control and Inform. Sci. 84, System Modeling and Optimisation. 12th IFIP Conference on system optimisation 1984 ( 1986) 866-878. | MR | Zbl

[16] G. Sonnevend and J. Stoer, Global ellipsoidal approximation and homotopy methods for solving convex analitic programs. Appl. Math. Optim. 21 ( 1990) 139-165. | MR | Zbl

[17] D.E. Stewart, Matrix Computation in C. University of Queensland, Australia ( 1992). ftp site: des@thrain.anu.edu.au. directory: pub/meschach

[18] L. Vandenberghe and S. Boyd, Semidefinite programming. SIAM Rev. 1 ( 1996) 49-95. | MR | Zbl

[19] J. Verschelde, P. Verlinden and R. Cools, Homotopy exploiting newton polytopes for solving sparse polynomials systems. SIAM J. Numer. Anal. 31 ( 1994) 915-930. | MR | Zbl

[20] A. Wright, Finding solutions to a system of polynomial equations. Math. Comp. 44 ( 1985) 125-133. | MR | Zbl