Task Embedded Coordinate Update: A Realizable Framework for Multivariate Non-convex Optimization

TL;DR

The paper introduces TECU, a unified framework embedding task-specific strategies into coordinate descent to efficiently optimize multivariate non-convex problems, with theoretical guarantees and practical effectiveness demonstrated through experiments.

Contribution

It proposes TECU, a novel framework integrating numerical algorithms and advanced techniques for non-convex optimization with error control and theoretical analysis.

Findings

TECU improves optimization efficiency and robustness.

Embedding ADMM and CNN enhances practical problem solving.

Experimental results confirm effectiveness and efficiency.

Abstract

We in this paper propose a realizable framework TECU, which embeds task-specific strategies into update schemes of coordinate descent, for optimizing multivariate non-convex problems with coupled objective functions. On one hand, TECU is capable of improving algorithm efficiencies through embedding productive numerical algorithms, for optimizing univariate sub-problems with nice properties. From the other side, it also augments probabilities to receive desired results, by embedding advanced techniques in optimizations of realistic tasks. Integrating both numerical algorithms and advanced techniques together, TECU is proposed in a unified framework for solving a class of non-convex problems. Although the task embedded strategies bring inaccuracies in sub-problem optimizations, we provide a realizable criterion to control the errors, meanwhile, to ensure robust performances with rigid theoretical analyses. By respectively embedding ADMM and a residual-type CNN in our algorithm framework, the experimental results verify both efficiency and effectiveness of embedding task-oriented strategies in coordinate descent for solving practical problems.