On the convergence of the proximal point algorithm for convex minimization
SIAM Journal on Control and Optimization
Proximal minimization algorithm with D-functions
Journal of Optimization Theory and Applications
Entropic proximal mappings with applications to nonlinear programming
Mathematics of Operations Research
Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
Mathematics of Operations Research
On the convergence of the exponential multiplier method for convex programming
Mathematical Programming: Series A and B
Entropy-like proximal methods in convex programming
Mathematics of Operations Research
A primal-dual potential reduction method for problems involving matrix inequalities
Mathematical Programming: Series A and B
Convergence rate analysis of nonquadratic proximal methods for convex and linear programming
Mathematics of Operations Research
Linear systems in Jordan algebras and primal-dual interior-point algorithms
Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
Convergence of Proximal-Like Algorithms
SIAM Journal on Optimization
An Interior Proximal Algorithm and the Exponential Multiplier Method for Semidefinite Programming
SIAM Journal on Optimization
Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
Mathematics of Operations Research
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We introduce an entropy-like proximal algorithm for the problem of minimizing a closed proper convex function subject to symmetric cone constraints. The algorithm is based on a distance-like function that is an extension of the Kullback-Leiber relative entropy to the setting of symmetric cones. Like the proximal algorithms for convex programming with nonnegative orthant cone constraints, we show that, under some mild assumptions, the sequence generated by the proposed algorithm is bounded and every accumulation point is a solution of the considered problem. In addition, we also present a dual application of the proposed algorithm to the symmetric cone linear program, leading to a multiplier method which is shown to possess similar properties as the exponential multiplier method (Tseng and Bertsekas in Math. Program. 60:1---19, 1993) holds.