Barrodale, I2020-01-162020-01-1619711971Barrodale, I. (1971). Best Rational Approximation and Strict Quasi-Convexity. MRC Technical Summary Report #1157.http://hdl.handle.net/1828/11492If a continuous function is strictly quasi-convex on a convex set $\Gamma $, then every local minimum of the function must be a global minimum. Furthermore, every local maximum of the function on the interior of $\Gamma $ must also be a global minimum. Here, we prove that any minimax rational approximation problem defines a strictly quasi-convex function with the property that a best approximation (if one exists) is a minimum of that function. The same result is not true in general for best rational approximation in other norms.enTechnical ReportDepartment of Computer Science