اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA counterexample to De Pierros conjecture on the convergence of under-relaxed cyclic projections
51
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The convex feasibility problem consists in finding a point in the intersection of a finite family of closed convex sets. When the intersection is empty, a best compromise is to search for a point that minimizes the sum of the squared distances to the sets. In 2001, de Pierro conjectured that the limit cycles generated by the $varepsilon$-under-relaxed cyclic projection method converge when $varepsilondownarrow 0$ towards a least squares solution. While the conjecture has been confirmed under fairly general conditions, we show that it is false in general by constructing a system of three compact convex sets in $mathbb{R}^3$ for which the $varepsilon$-under-relaxed cycles do not converge.
قيم البحث
اقرأ أيضاً
We prove that the Laptev--Safronov conjecture (Comm. Math. Phys., 2009) is false in the range that is not covered by Franks positive result (Bull. Lond. Math. Soc., 2011). The simple counterexample is adaptable to a large class of Schrodinger type op
erators, for which we also prove new sharp upper bounds.
The alternating direction method of multipliers (ADMM) is a popular method for solving convex separable minimization problems with linear equality constraints. The generalization of the two-block ADMM to the three-block ADMM is not trivial since the
three-block ADMM is not convergence in general. Many variants of three-block ADMM have been developed with guarantee convergence. Besides the ADMM, the alternating minimization algorithm (AMA) is also an important algorithm for solving the convex separable minimization problem with linear equality constraints. The AMA is first proposed by Tseng, and it is equivalent to the forward-backward splitting algorithm applied to the corresponding dual problem. In this paper, we design a variant of three-block AMA, which is derived by employing an inertial extension of the three-operator splitting algorithm to the dual problem. Compared with three-block ADMM, the first subproblem of the proposed algorithm only minimizing the Lagrangian function. As a by-product, we obtain a relaxed algorithm of Davis and Yin. Under mild conditions on the parameters, we establish the convergence of the proposed algorithm in infinite-dimensional Hilbert spaces. Finally, we conduct numerical experiments on the stable principal component pursuit (SPCP) to verify the efficiency and effectiveness of the proposed algorithm.
Let A be a finite dimensional, unital, and associative algebra which is endowed with a non-degenerate and invariant inner product. We give an explicit description of an action of cyclic Sullivan chord diagrams on the normalized Hochschild cochain com
plex of A. As a corollary, the Hochschild cohomology of A becomes a Frobenius algebra which is endowed with a compatible BV operator. If A is also commutative, then the discussion extends to an action of general Sullivan chord diagrams. Some implications of this are discussed.
Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoffmann-Ostenhof and Nadirashvili proved this to be false by constructing
a counterexample in the plane with many holes and raised the question of the minimum number of holes a counterexample can have. In this paper we prove it is at most 6.
Makienkos conjecture, a proposed addition to Sullivans dictionary, can be stated as follows: The Julia set of a rational function R has buried points if and only if no component of the Fatou set is completely invariant under the second iterate of R.
We prove Makienkos conjecture for rational functions with Julia sets that are decomposable continua. This is a very broad collection of Julia sets; it is not known if there exists a rational functions whose Julia set is an indecomposable continuum.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
