legendre-fenchel conjugate

A note on Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms

  • Hsia Yong
    • Categories Global Optimization Theory, Unconstrained Optimization Tags ,

    The Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms was posted as an open question in the field of nonlinear analysis and optimization by Hiriart-Urruty [`Question 11′ in {\it SIAM Review} 49, 255-273, (2007)]. Under a convex assumption on the function, it was answered by Zhao [SIAM J. Matrix Analysis $\&$ Applications, 31(4), … Read more

    The Legendre-Fenchel Conjugate of the Product of Two positive definite Quadratic Forms

  • Yun-Bin Zhao
    • Categories Convex Optimization Tags , , ,

    It is well-known that the Legendre-Fenchel conjugate of a positive definite quadratic form can be explicitly expressed as another positive definite quadratic form, and that the conjugate of the sum of several positive definite quadratic forms can be expressed via inf-convolution. However, the Legendre-Fenchel conjugate of the product of two positive definite quadratic forms is … Read more