Heinz H. Bauschke, Patrick L. Combettes
Abstract
The theory of convex functions is most powerful in the presence of lower semicontinuity. A key property of lower semicontinuous convex functions is the existence of a continuous affine minorant, which we establish in this chapter by projecting onto the epigraph of the function.
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The theory of convex functions is most powerful in the presence of lower semicontinuity. A key property of lower semicontinuous convex functions is the existence of a continuous affine minorant, which we establish in this chapter by projecting onto the epigraph of the function.
Key concepts: Epigraph, Affine transformation, Regular polygon, Pseudoconvex function, Mathematics, Convex function, Property (philosophy), Pure mathematics