Interior Proximal and Multiplier Methods Based on Second Order Homogeneous Kernels

References

• Auslender A. , Cominetti R. , Haddou M. Asymptotic analysis of penalty and barrier methods in convex and linear programming. Math. Oper. Res. (1997) 22 43 62 Link, Google Scholar
• Auslender A. , Haddou M. An interior proximal method for convex linearly constrained problems and its extension to variational inequalities. Math. Programming (1995) 71 77 100 Crossref, Google Scholar
• Auslender A. , Teboulle M. , Ben-Tiba S. A logarithmic-quadratic proximal method for variational inequalities. Comput. Optim. Appl. (1999) 12 31 40 Crossref, Google Scholar
• Ben-Tal A. , Zibulevsky M. Penalty-barrier methods for convex programming problems. SIAM J. Optim. (1997) 7 347 366 Crossref, Google Scholar
• Bertsekas D. Constrained Optimization and Lagrange Multiplier Methods (1982) (Academic Press, New York) Google Scholar
• Eggermont P. P. B. Multiplicatively iterative algorithms for convex programming. Linear Algebra Appl. (1990) 130 25 42 Crossref, Google Scholar
• Fiacco A. V. , McCormick G. P. Nonlinear Programming: Sequential Unconstrained Minimization Techniques (1990) (Classics in Applied Mathematics, SIAM, Philadelphia, PA) Crossref, Google Scholar
• Güler O. On the convergence of the proximal point algorithm for convex minimization. SIAM J. Control Optim. (1991) 29 403 419 Crossref, Google Scholar
• Iusem A. N. , Svaiter B. , Teboulle M. Entropy-like proximal methods in convex programming. Math. Oper. Res. (1994) 19 790 814 Link, Google Scholar
• Iusem A. N. , Teboulle M. Convergence rate analysis of nonquadratic proximal and augmented Lagrangian methods for convex and linear programming. Math. Oper. Res. (1995) 20 657 677 Link, Google Scholar
• Kiwiel K. C. Proximal minimization methods with generalized Bregman functions. SIAM J. Control Optim. (1997) 35 1142 1168 Crossref, Google Scholar
• Knopp K. Infinite Sequences and Series (1956) (Dover Publications, Inc., New York) Google Scholar
• Lemaire B. , Penot J. P. The proximal algorithm. International Series of Numerical Mathematics (1989) (Birkhauser Verlag, Basel, Switzerland) 73 87 Google Scholar
• Lemaire B. , Durier R. , Michelot C. On the convergence of some iterative methods for convex minimization. Lecture Notes in Economics and Mathematical Systems (1995) 429 (Springer Verlag, New York) 252 268 Crossref, Google Scholar
• Martinet B. Regularisation d'inéquations variationnelles par approximations successive. Rev. Francaise d'Automatique et Inform. Rech. Opér. (1970) 4 154 159 Google Scholar
• Moreau J. J. Proximité et dualité dans un espace Hilbertien. Bull. Soc. Math. France (1965) 93 273 299 Crossref, Google Scholar
• Nesterov Y. , Nemirovski A. Interior Point Polynomial Algorithms in Convex Programming (1994) (SIAM Publications, Philadelphia, PA) Crossref, Google Scholar
• Polyak B. T. Introduction to Optimization (1987) (Optimization Software Inc., New York) Google Scholar
• Polyak R. A. Modified barrier functions (theory and methods). Math. Programming (1992) 54 177 222 Crossref, Google Scholar
• Polyak R. A. , Teboulle M. Nonlinear rescaling and proximal-like methods in convex optimization. Math. Programming (1997) 76 265 284 Crossref, Google Scholar
• Rockafellar R. T. Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Rockafellar R. T. A dual approach to solving nonlinear programming problems by unconstrained minimization. Math. Programming (1973) 5 354 373 Crossref, Google Scholar
• Rockafellar R. T. Monotone operators and the proximal point algorithm. SIAM J. Control Optim. (1976) 14 877 898 Crossref, Google Scholar
• Teboulle M. Entropic proximal mappings with application to nonlinear programming. Math. Oper. Res. (1992) 17 670 690 Link, Google Scholar
• Teboulle M. Convergence of proximal-like algorithms. SIAM J. Optim. (1997) 7 1069 1083 Crossref, Google Scholar
• Tseng P. , Bertsekas D. On the convergence of the exponential multiplier method for convex programming. Math. Programming (1993) 60 1 19 Crossref, Google Scholar