A non-interior-point continuation method for linear complementarity problems
SIAM Journal on Matrix Analysis and Applications
Some Noninterior Continuation Methods for LinearComplementarity Problems
SIAM Journal on Matrix Analysis and Applications
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
Merit functions for semi-definite complementarity problems
Mathematical Programming: Series A and B
On Homotopy-Smoothing Methods for Box-Constrained Variational Inequalities
SIAM Journal on Control and Optimization
Beyond Monotonicity in Regularization Methods for Nonlinear Complementarity Problems
SIAM Journal on Control and Optimization
Associative and Jordan Algebras, and Polynomial Time Interior-Point Algorithms for Symmetric Cones
Mathematics of Operations Research
Semidefinite Programs: New Search Directions, Smoothing-Type Methods, and Numerical Results
SIAM Journal on Optimization
A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm
SIAM Journal on Optimization
SIAM Journal on Optimization
Computational Optimization and Applications
Semismooth Matrix-Valued Functions
Mathematics of Operations Research
SIAM Journal on Optimization
An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
Mathematical Programming: Series A and B
Computational Optimization and Applications
Journal of Global Optimization
Mathematics of Operations Research
SIAM Journal on Optimization
SIAM Journal on Optimization
Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
Mathematics of Operations Research
A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems
Optimization Methods & Software
A Globally Convergent Smoothing Method for Symmetric Conic Linear Programming
ISICA '09 Proceedings of the 4th International Symposium on Advances in Computation and Intelligence
A generalized Newton method for absolute value equations associated with second order cones
Journal of Computational and Applied Mathematics
A new smoothing Newton method for symmetric cone complementarity problems
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Computers & Mathematics with Applications
A Continuation Method for Nonlinear Complementarity Problems over Symmetric Cones
SIAM Journal on Optimization
A full-Newton step non-interior continuation algorithm for a class of complementarity problems
Journal of Computational and Applied Mathematics
Polynomial time solvability of non-symmetric semidefinite programming
Operations Research Letters
Stationary point conditions for the FB merit function associated with symmetric cones
Operations Research Letters
A fixed-point method for a class of super-large scale nonlinear complementarity problems
Computers & Mathematics with Applications
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There recently has been much interest in studying optimization problems over symmetric cones. In this paper, we first investigate a smoothing function in the context of symmetric cones and show that it is coercive under suitable assumptions. We then extend two generic frameworks of smoothing algorithms to solve the complementarity problems over symmetric cones, and prove the proposed algorithms are globally convergent under suitable assumptions. We also give a specific smoothing Newton algorithm which is globally and locally quadratically convergent under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool which is extensively used in our analysis. Preliminary numerical results for second-order cone complementarity problems are reported.