The infimal convolution
WebMar 1, 2024 · Infimal Convolution Moreau Envelope Proximal Operator Continuous Affine Minorant Firmly Nonexpansive These keywords were added by machine and not by the … WebApr 14, 2024 · Convex conjugate of sum of convex functions — infimal convolution Asked 10 months ago Modified 10 months ago Viewed 207 times 2 I have a function f: R → R + defined by f ( x) = f 1 ( x) + f 2 ( x) + f 3 ( x) − f 4 ( x) where every f i is a proper, closed convex function defined over some interval [ a, b] ⊂ R. I would like to minimize f
The infimal convolution
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http://www.lukoe.com/finance/quantNotes/Infimal_convolution_.html WebFeb 1, 2024 · Convolution Subdifferentiation of the Infimal Convolution and Minimal Time Problems February 2024 Authors: Abderrahim Hantoute Taron Zakaryan Bloom Social Analytics Abstract We investigate in...
WebJan 1, 2011 · Abstract. This chapter is devoted to a fundamental convexity-preserving operation for functions: the infimal convolution. Its properties are investigated, with … WebAug 1, 2016 · The infimal-convolution functional itself optimally balances both components and provides a first component , with less dynamic information due to high temporal regularity, and a second component v, with more dynamic change. As we will see, such an optimal balancing comprises a flexible but tailored convex spatio-temporal regularization ...
The infimal convolution (or epi-sum) of two functions and is defined as. Let be proper, convex and lower semicontinuous functions on Then the infimal convolution is convex and lower semicontinuous (but not necessarily proper), [2] and satisfies. See more In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–Fenchel … See more The convex conjugate of a closed convex function is again a closed convex function. The convex conjugate of a polyhedral convex function (a convex function with polyhedral See more • Touchette, Hugo (2014-10-16). "Legendre-Fenchel transforms in a nutshell" (PDF). Archived from the original (PDF) on 2024-04-07. Retrieved 2024-01-09. • Touchette, Hugo (2006-11-21). "Elements of convex analysis" (PDF). Archived from the original (PDF) … See more For more examples, see § Table of selected convex conjugates. • The convex conjugate of an affine function $${\displaystyle f(x)=\left\langle a,x\right\rangle -b}$$ is f ∗ ( x ∗ ) = { b , x ∗ = a + ∞ , x ∗ ≠ a . {\displaystyle f^{*}\left(x^{*}\right)={\begin{cases}b,&x^… • Dual problem • Fenchel's duality theorem • Legendre transformation • Young's inequality for products See more WebThe goal of this work was to develop a regularization method using the infimal convolution of the first- and the second-order derivatives to reduce or even prevent staircase artifacts in the reconstructed images, and to investigate if the advantage in noise suppression by this TV-type regularization can be translated into dose reduction.
WebApr 3, 2011 · This operator admits a very precise micro-economic interpretation: if several production units produce the same output, the Infimal Convolution of their cost functions …
WebThe infimal convolution of oscillation TGV with respect to several directions and scales is then used to model images with structured oscillatory texture. Such functionals constitute a regularizer with good texture preservation properties and can flexibly be incorporated into many imaging problems. We give a detailed theoretical analysis of the ... foreground midground backgroundWebIn this well-written paper on infimal convolution the author's purpose is "to provide a survey of the subject as well as to complement or sharpen existing results". The author has … foreground notification flutterWebAug 9, 2024 · Under well-posedness conditions we establish an inclusion for the Mordukhovich limiting subdifferential of the marginal function and obtain new properties and descriptions of the Fréchet, proximal and Mordukhovich limiting subdifferentials of the infimal convolution. foreground object