Duality relationships for entropy-like minimization problems

@article{Borwein1991DualityRF,
  title={Duality relationships for entropy-like minimization problems},
  author={J. Borwein and A. Lewis},
  journal={Siam Journal on Control and Optimization},
  year={1991},
  volume={29},
  pages={325-338}
}
  • J. Borwein, A. Lewis
  • Published 1991
  • Mathematics
  • Siam Journal on Control and Optimization
  • This paper considers the minimization of a convex integral functional over the positive cone of an $L_p $ space, subject to a finite number of linear equality constraints. Such problems arise in spectral estimation, where the bjective function is often entropy-like, and in constrained approximation. The Lagrangian dual problem is finite-dimensional and unconstrained. Under a quasi-interior constraint qualification, the primal and dual values are equal, with dual attainment. Examples show the… CONTINUE READING
    220 Citations
    Minimization of entropy functionals revisited
    • I. Csiszár, F. Matús
    • Mathematics, Computer Science
    • 2012 IEEE International Symposium on Information Theory Proceedings
    • 2012
    • 3
    • PDF
    Minimizers of energy functionals
    • 37
    • PDF
    Generalized Minimizers of Convex Integral Functionals and Pythagorean Identities
    • 1
    • PDF
    Convex minimization problems with weak constraint qualifications
    • 11
    • PDF
    Minimization of entropy functionals
    • 23
    • PDF
    Double Smoothing Technique for Large-Scale Linearly Constrained Convex Optimization
    • 66
    • PDF
    A Note on Cores and Quasi Relative Interiors in Partially Finite Convex Programming

    References

    SHOWING 1-10 OF 20 REFERENCES
    Partially finite convex programming, Part II: Explicit lattice models
    • 99
    • PDF
    A dual approach to multidimensional L p spectral estimation problems
    • 34
    • Highly Influential
    Integrals which are convex functionals. II
    • 468
    • PDF
    Conjugate Duality and Optimization
    • R Tyrrell Rockafellar
    • 1974
    • 215
    • PDF
    $L_2 $ Spectral Estimation
    • 38
    Real and complex analysis
    • W. Rudin
    • Mathematics, Computer Science
    • 1966
    • 7,361
    • PDF