Symbiosis between Linear Algebra and Optimization

The efficiency and effectiveness of most optimization algorithms hinges on the numerical linearalgebra algorithms that they utilize. Effective linearalgebra is crucial to their success, and because of this, optimization applications have motivated fundamental advances in numerical linearalgebra. This essay will highlight contributions of numerical linearalgebra to optimization, as well as some optimization problems encountered within linearalgebra that contribute to a symbiotic relationship.