scholarly journals A learning-enhanced projection method for solving convex feasibility problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Janosch Rieger ◽  
Keyword(s):  
Projection Method ◽  
Convex Feasibility Problems ◽  
Convex Feasibility

CONVERGENCE OF MANN’S ALTERNATING PROJECTIONS IN CAT() SPACES

2018 ◽  
Vol 98 (1) ◽  
pp. 134-143 ◽  
Author(s):  
BYOUNG JIN CHOI
Keyword(s):  
Strong Convergence ◽  
Projection Method ◽  
Convex Feasibility Problem ◽  
Feasibility Problem ◽  
Alternating Projections ◽  
Normed Spaces ◽  
Closed Sets ◽  
Convex Feasibility ◽  
Alternating Projection ◽  
Iterative Projection Method

We study the convex feasibility problem in$\text{CAT}(\unicode[STIX]{x1D705})$spaces using Mann’s iterative projection method. To do this, we extend Mann’s projection method in normed spaces to$\text{CAT}(\unicode[STIX]{x1D705})$spaces with$\unicode[STIX]{x1D705}\geq 0$, and then we prove the$\unicode[STIX]{x1D6E5}$-convergence of the method. Furthermore, under certain regularity or compactness conditions on the convex closed sets, we prove the strong convergence of Mann’s alternating projection sequence in$\text{CAT}(\unicode[STIX]{x1D705})$spaces with$\unicode[STIX]{x1D705}\geq 0$.

Order Reduction of Controller Based on LMIs Improving Error Bounds

1997 ◽  
Author(s):  
Roberd Saragih ◽  
Yoshida Kazuo
Keyword(s):  
Projection Method ◽  
Order Reduction ◽  
Feasibility Problem ◽  
Closed Loop System ◽  
Reduced Order ◽  
Bounded Real Lemma ◽  
Convex Feasibility ◽  
Alternating Projection ◽  
Alternating Projection Method ◽  
Order Reduction Method

Abstract In this paper, we propose an order reduction method of controller based on combination of the alternating projection method and the balanced truncation. In this method both the errors of controller and the closed-loop system caused by the reduced-order controller can be improved simultaneously. By using a generalized Bounded Real Lemma, a feasible reduced-order controller can be derived. The sufficient condition for the existence of a reduced-order controller leads to a non-convex feasibility problem. To solve the problem, we can use an improved computational scheme based on the alternating projection method. But it is needed so much time to solve the problem if compared by the other methods. To validate the proposed method, some numerical calculations and simulations are carried out.

Iterative approaches to convex feasibility problems in Banach spaces

2006 ◽  
Vol 64 (9) ◽  
pp. 2022-2042 ◽  
Author(s):  
John G. O’Hara ◽  
Paranjothi Pillay ◽  
Hong-Kun Xu
Keyword(s):  
Banach Spaces ◽  
Convex Feasibility Problems ◽  
Convex Feasibility
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