O'Leary, Dianne P.The efficiency and effectiveness of most optimization algorithms hinges on the numerical linear algebra algorithms that they utilize. Effective linear algebra is crucial to their success, and because of this, optimization applications have motivated fundamental advances in numerical linear algebra. This essay will highlight contributions of numerical linear algebra to optimization, as well as some optimization problems encountered within linear algebra that contribute to a symbiotic relationship. Also cross-referenced as UMIACS-TR-99-30en-USTechnical Report