x, y \in C \implies t x + (1-t) y \in C, \quad \text{for all $t \in [0,1]$}. joining $x$ and $y$ lies entirely in $C$. See Figure \ref{fig:convex_set}. A \emph{convex ...
Transactions of the American Mathematical Society, Vol. 327, No. 2 (Oct., 1991), pp. 795-813 (19 pages) Let Γ(X) denote the proper, lower semicontinuous, convex functions on a Banach space X, equipped ...
Convex Geometry is the branch of geometry studying convex sets, mainly in Euclidean spaces. Convex sets occur naturally in Geometry and in many mathematical areas: computational geometry, convex ...
Convex optimisation constitutes a fundamental area in applied mathematics where the objective is to identify the minimum of a convex function subject to a set of convex constraints. This framework ...
Abstract: This chapter helps the students to identify convex functions, convex sets, and convex optimization problems. It presents comparison between a convex and a non‐convex function. The chapter ...
In the convex [[optimisation method]], we use a convex surrogate $\ell$ of the 0-1 loss function. $$\arg \min_{h \in H} \frac{1}{n} \sum_{i=1}^n l(X_i, Y_i, h) $$ This is because the 0-1 loss function ...
Mathematics of Operations Research, Vol. 34, No. 4 (Nov., 2009), pp. 869-879 (11 pages) Consider the supposedly simple problem of computing a point in a convex set that is conveyed by a separation ...
Abstract: This chapter helps the students to identify convex functions, convex sets, and convex optimization problems. It presents comparison between a convex and a non‐convex function. The chapter ...
To solve the problem on inaccuracy when estimating the point spread function (PSF) of the ideal original image in traditional projection onto convex set (POCS) super-resolution (SR) reconstruction, ...
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