Nonlinear functional analysis and its applications
Nonlinear functional analysis and its applications
On the convergence of Han's method for convex programming with quadratic objective
Mathematical Programming: Series A and B
Digital processing of random signals: theory and methods
Digital processing of random signals: theory and methods
Alternating convex projection methods for discrete-time covariance control design
Journal of Optimization Theory and Applications
Matrix computations (3rd ed.)
Strong Convergence of Block-Iterative Outer Approximation Methods for Convex Optimization
SIAM Journal on Control and Optimization
Convex analysis and variational problems
Convex analysis and variational problems
Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics
Hard-constrained inconsistent signal feasibility problems
IEEE Transactions on Signal Processing
Learning averages over the lie group of symmetric positive-definite matrices
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
An algorithm to compute averages on matrix Lie groups
IEEE Transactions on Signal Processing
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This paper studies the problem of finding the nearest symmetric positive definite Toeplitz matrix to a given symmetric one. Additional design constraints, which are also formed as closed convex sets in the real Hilbert space of all symmetric matrices, are imposed on the desired matrix. An algorithmic solution to the problem given by the hybrid steepest descent method is established also in the case of inconsistent design constraints.