References
- Martinet B. Régularisation d’in\’{q}uations variationelles par approximations successives. Reveu d’ Automatique Informatique et Reserche Opérationelle. 1970;4(R3):154–158.
- Censor Y, Zenios S. The proximal minimization algorithm with d-functions. J Optim Theory Appl. 1992;73:451–464.
- Chen G, Teboulle M. Convergence analysis of a proximal-like minimization algorithm using bregman’s function. SIAM J Optim. 1993;3(3):538–543.
- Pan S, Chen J. A class of interior proximal-like algorithms for convex second-order cone programming. SIAM J Optim. 2008;19(2):883–910.
- Pan S, Chen J. Proximal-like algorithm using the quasi D-function for convex second-order cone programming. J Optim Theory Appl. 2008;138:95–113.
- Pan S, Chen J. Interior proximal methods and central paths for convex second-order cone programming. Nonlinear Anal: Theory Methods Appl. 2010;73(9):3083–3100.
- Doljansky M, Teboulle M. An interior proximal algorithm and the exponential multiplier method for semidefinite programming. SIAM J Optim. 1998;9(1):1–13.
- Auslender A, Teboulle M. Interior gradient and proximal methods for convex and conic optimization. SIAM J Optim. 2006;16(3):697–725.
- Teboulle M. Entropic proximal mappings with applications to nonlinear programming. Math Oper Res. 1992;17(3):670–690.
- Teboulle M. Convergence of proximal-like algorithms. SIAM J Optim. 1997;7(4):1069–1083.
- Auslender A, Teboulle M, Ben-Tiba S. Interior proximal and multiplier methods based on second order homogeneous functionals. Math Oper Res. 1999;24(3):645–668.
- Auslender A, Silva P, Teboulle M. Nonmonotone projected gradient methods based on barrier and euclidean distances. Comput Optim Appl. 2007;38:305–327.
- Auslender A, Teboulle M. Projected subgradient methods with non-euclidean distances for non-differentiable convex minimization and variational inequalities. Math Program. 2009;120(1):27–48.
- Villacorta K, Oliveira P. An interior proximal method in vector optimization. Eur J Oper Res. 2011;214(3):485–492.
- Papa Quiroz E, Oliveira P. An extension of proximal methods for quasiconvex minimization on the nonnegative orthant. Eur J Oper Res. 2012;216:26–32.
- Papa Quiroz E, Mallma Ramirez L, Oliveira P. An inexact proximal method for quasiconvex minimization. Eur J Oper Res. 2015;246:721–729.
- Sarmiento O. Papa Quiroz E, Oliveira P. A proximal multiplier method for separable convex minimization. Optimization. 2016;65(2):501–537.
- Liese F, Vajda I. Convex statistical distances. Leipzig: Teubner; 1987.
- Faraut J, Korányi A. Analysis on symmetric cones. New York (NY): The Clarendon Press, Oxford University Press, Oxford Science Publications; 1994. (Oxford mathematical monographs).
- Chen J, Pan S. An entropy-like proximal algorithm and the exponential multiplier method for convex symmetric cone programming. Comput Optim Appl. 2010;47(3):477–499.
- Yu Z, Zhu Y, Cao Q. On the convergence of central path and generalized proximal point method for symmetric cone linear programming. Appl Math Inf Sci. 2013;7:2327–2333.
- Faybusovich L. Euclidean jordan algebras and interior-point algorithms. Positivity. 1997;1(4):331–357.
- Faybusovich F. Linear systems in jordan algebras and primal-dual interior-point algorithms. J Comput Appl Math. 1997;86(1):149–175.
- Schmieta S, Alizadeh F. Extension of primal-dual interior point algorithms to symmetric cones. Math Program. 2003;96(3):409–438.
- Gu G, Zangiabadi M, Roos C. Full nesterov-todd step infeasible interior-point method for symmetric optimization. Eur J Oper Res. 2011;214(3):473–484.
- Wang G, Bai Y. A new full nesterov-todd step primal-dual path- following interior-point algorithm for symmetric optimization. J Optim Theory Appl. 2012;154(3):966–985.
- Valkonen T. Extension of primal-dual interior point methods to diff-convex problems on symmetric cones. Optimization. 2013;62(3):345–377.
- Wang G, Yu C, Teo K. A new full nesterov-todd step feasible interior-point method for convex quadratic symmetric cone optimization. Appl Math Comput. 2013;221:329–343.
- Wang G, Zhang Z, Zhu D. On extending primal-dual interior-point method for linear optimization to convex quadratic symmetric cone optimization. Numer Funct Anal Optim. 2013;34(5):576–603.
- Ramírez H, Sossa D. On the central paths in symmetric cone programming. J Optim Theory Appl. in press 2016.
- Roos C, Terlaky T, Vial J. Theory and algorithms for linear optimization: an interior-point approach. New York (NY): Wiley; 1997. (Wiley-Interscience series in discrete mathematics and optimization).
- Alvarez F, López J. Interior proximal bundle algorithm with variable metric for nonsmooth convex symmetric cone programming. Optimization. 2016;65(9):1757–1779.
- Alvarez F, López J, Ramírez CH. Interior proximal algorithm with variable metric for second-order cone programming: applications to structural optimization and support vector machines. Optim Methods Softw. 2010;25(6):859–881.
- Baes M. Convexity and differentiability properties of spectral functions and spectral mappings on euclidean jordan algebras. Linear Algebra Appl. 2007;422(2–3):664–700.
- Sun D, Sun J. Löwner’s operator and spectral functions in euclidean jordan algebras. Math Oper Res. 2008;33(2):421–445.
- Rockafellar R. Convex analysis. Princeton (NJ): Princeton University Press; 1970. (Princeton mathematical series).
- Alizadeh F, Goldfarb D. Second-order cone programming. Math. Program. 2003;95:3–51.
- Bauschke H, Borwein J. Legendre functions and the method of random bregman projections. J Convex Anal. 1997;4(1):27–68.
- Chang Y, Chen J, Pan S. Symmetric cone monotone functions and symmetric cone convex functions. J Nonlinear Convex Anal. 2016;17(3):499–512.
- Chen J. The convex and monotone functions associated with second-order cone. Optimization. 2006;55(4):363–385.
- Kaplan A, Tichatschke R. Interior proximal method for variational inequalities on non-polyhedral sets. Discussiones Mathematicae: Differ Inclusions Control Optim. 2007;27(1):71–93.
- Iusem A, Svaiter B, Teboulle M. Entropy-like proximal methods in convex programming. Math Oper Res. 1994;19(4):790–814.
- Csiszar I. An axiomatic approach to inference for linear inverse problems. Ann. Stat. 1991;19(4):2032–2066.
- Kaplan A, Tichatschke R. On inexact generalized proximal methods with a weakened error tolerance criterion. Optimization. 2004;53(1):3–17.
- Iusem A, Svaiter B, da Cruz Neto J. Central paths, generalized proximal point methods and cauchy trajectories in riemannian manifolds. SIAM J Control Optim. 1999;37(2):566–588.
- Chang Y, Chen J. Convexity of symmetric cone trace functions in euclidean jordan algebras. J Nonlinear Convex Anal. 2013;14(1):53–61.