In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph between the two points. …

A function f in one variable de ned on an interval I R is convex if f 00(x) 0 for all x 2I, and concave if f 00(x) 0 for all x 2I. The graph of convex and concave function have the following shapes: …

Forty-first International Conference on Machine Learning (Best Paper at …

In the previous couple of lectures, we’ve been focusing on the theory of convex sets. In this lecture, we shift our focus to the other important player in convex optimization, namely, convex …

2022年12月7日 · NAME OOQP - A package for solving convex quadratic programming problems. SYNOPSIS This directory contains OOQP, a package for solving convex quadratic …

Theorem 1.10 (Jensen’s Inequality). For a convex function fon the interval I, let x 1;x 2; ;x n2Iand 1; 2; ; n2(0;1) satisfying P n j=1 j = 1. Then f( 1x 1 + + nx n) 1f(x 1) + + nf(x n): When f is …

This is just a quick and condensed note on the basic definitions and characterizations of concave, convex, quasiconcave and (to some extent) quasiconvex functions, with some examples. …

Convex functions have another obvious property, which is related to the location of the tangent to the graph of the function. The function \(f\left( x \right)\) is convex downward on the interval …

In applications, we encounter many constrained optimization problems. Examples. The constrained can be a convex set C. That is. 0 if x 2 C +1 otherwise . For more applications, …

Almost every convex function can be expressed as the pointwise supremum of a family of affine functions. / h = ∑ on is concave for 0 1, and its extension is nondecreasing. If is concave and...