Adaptive multi-gradient methods for quasiconvex vector optimization and
  applications to multi-task learning
Nguyen Anh Minh Le Dung Muu Tran Ngoc Thang
We present an adaptive step-size method, which does not include line-search
techniques, for solving a wide class of nonconvex multiobjective programming
problems on an unbounded constraint set. We also prove convergence of a general
approach under modest assumptions. More specifically, the convexity criterion
might not be satisfied by the objective function. Unlike descent line-search
algorithms, it does not require an initial step-size to be determined by a
previously determined Lipschitz constant. The process's primary characteristic
is its gradual step-size reduction up until a predetermined condition is met.
It can be specifically applied to offer an innovative multi-gradient projection
method for unbounded constrained optimization issues. Preliminary findings from
a few computational examples confirm the accuracy of the strategy. We apply the
proposed technique to some multi-task learning experiments to show its efficacy
for large-scale challenges.