Felix Lieder

Variance Reduction of Stochastic Gradients Without Full Gradient Evaluation

  • Florian Jarre
  • Felix Lieder
    • Categories Unconstrained Optimization Tags ,

    A standard concept for reducing the variance of stochastic gradient approximations is based on full gradient evaluations every now and then. In this paper an approach is considered that — while approximating a local minimizer of a sum of functions — also generates approximations of the gradient and the function values without relying on full … Read more

    Set-Completely-Positive Representations and Cuts for the Max-Cut Polytope and the Unit Modulus Lifting

  • Florian Jarre
  • Ya-Feng Liu
  • Felix Lieder
  • Cheng Lu
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    This paper considers a generalization of the “max-cut-polytope” $\conv\{\ xx^T\mid x\in\real^n, \ \ |x_k| = 1 \ \hbox{for} \ 1\le k\le n\}$ in the space of real symmetric $n\times n$-matrices with all-ones-diagonal to a complex “unit modulus lifting” $\conv\{xx\HH\mid x\in\complex^n, \ \ |x_k| = 1 \ \hbox{for} \ 1\le k\le n\}$ in the space of … Read more

    The solution of Euclidean norm trust region SQP subproblems via second order cone programs, an overview and elementary introduction

  • Florian Jarre
  • Felix Lieder
    • Categories Constrained Nonlinear Optimization, Second-Order Cone Programming Tags , ,

    It is well known that convex SQP subproblems with a Euclidean norm trust region constraint can be reduced to second order cone programs for which the theory of Euclidean Jordan-algebras leads to efficient interior-point algorithms. Here, a brief and self-contained outline of the principles of such an implementation is given. All identities relevant for the … Read more