Area-time complexity of the unconstrained minimization problem

CALCOLO ◽  
1986 ◽  
Vol 23 (2) ◽  
pp. 175-184 ◽  
Author(s):  
B. Codenotti ◽  
P. Favati
Keyword(s):  
Minimization Problem ◽  
Time Complexity ◽  
Unconstrained Minimization ◽  
Unconstrained Minimization Problem

Hybrid spectral gradient method for the unconstrained minimization problem

2008 ◽  
Vol 44 (2) ◽  
pp. 193-212 ◽  
Author(s):  
William La Cruz ◽  
Gilberto Noguera
Keyword(s):  
Minimization Problem ◽  
Gradient Method ◽  
Unconstrained Minimization ◽  
Spectral Gradient Method ◽  
Unconstrained Minimization Problem

A minimization algorithm for fuzzy top-down tree automata over lattices

2020 ◽  
pp. 1-10
Author(s):  
M. Ghorani ◽  
S. Garhwal
Keyword(s):  
Minimization Problem ◽  
Time Complexity ◽  
Tree Automaton ◽  
Tree Automata ◽  
Minimization Algorithm ◽  
Top Down ◽  
Minimal Form ◽  
Minimization Algorithms ◽  
The Given

In this paper, we study fuzzy top-down tree automata over lattices ( LTA s , for short). The purpose of this contribution is to investigate the minimization problem for LTA s . We first define the concept of statewise equivalence between two LTA s . Thereafter, we show the existence of the statewise minimal form for an LTA . To this end, we find a statewise irreducible LTA which is equivalent to a given LTA . Then, we provide an algorithm to find the statewise minimal LTA and by a theorem, we show that the output statewise minimal LTA is statewise equivalent to the given input. Moreover, we compute the time complexity of the given algorithm. The proposed algorithm can be applied to any given LTA and, unlike some minimization algorithms given in the literature, the input doesn’t need to be a complete, deterministic, or reduced lattice-valued tree automaton. Finally, we provide some examples to show the efficiency of the presented algorithm.

scholarly journals Stable Approximations of a Minimal Surface Problem with Variational Inequalities

1997 ◽  
Vol 2 (1-2) ◽  
pp. 137-161 ◽  
Author(s):  
M. Zuhair Nashed ◽  
Otmar Scherzer
Keyword(s):  
Dirichlet Problem ◽  
Variational Inequalities ◽  
Minimal Surface ◽  
Unconstrained Minimization ◽  
Trace Operator ◽  
Functions Of Bounded Variation ◽  
New Approach ◽  
Regularization Procedure ◽  
Unconstrained Minimization Problem ◽  
Stable Approximation

In this paper we develop a new approach for the stable approximation of a minimal surface problem associated with a relaxed Dirichlet problem in the spaceBV(Ω)of functions of bounded variation. The problem can be reformulated as an unconstrained minimization problem of a functional𝒥onBV(Ω)defined by𝒥(u)=𝒜(u)+∫∂Ω|Tu−Φ|, where𝒜(u)is the “area integral” ofuwith respect toΩ,Tis the “trace operator” fromBV(Ω)intoL i(∂Ω), andϕis the prescribed data on the boundary ofΩ. We establish convergence and stability of approximate regularized solutions which are solutions of a family of variational inequalities. We also prove convergence of an iterative method based on Uzawa's algorithm for implementation of our regularization procedure.

Blind Deconvolution of Atmospherically Degraded Infrared Images Using Normalized Sparsity Measure

2013 ◽  
Vol 347-350 ◽  
pp. 297-301
Author(s):  
Dong Jie Tan ◽  
An Zhang
Keyword(s):  
Minimization Problem ◽  
Blind Deconvolution ◽  
Unconstrained Minimization ◽  
Real Data ◽  
Image Deblurring ◽  
Latent Image ◽  
Blind Image Deblurring ◽  
Symmetric Constraint ◽  
Sparse Prior ◽  
Blind Image

Blind image deblurring from a single image is a highly ill-posed problem. To tackle this problem, prior knowledge about the point spread function (PSF) and latent image are required. In this paper, a blind image deblurring approach is proposed to remove atmospheric blur, which utilizes the normalized sparse prior on the latent image and radial symmetric constraint on PSF. By introducing an expanding operator, the original constrained minimization problem is simplified to an unconstrained minimization problem and it therefore can be solved efficiently. Experiments on both synthetic and real data demonstrate the effectiveness of our approach.

scholarly journals Deblurring by Solving a TVp-Regularized Optimization Problem Using Split Bregman Method

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Su Xiao
Keyword(s):  
Minimization Problem ◽  
Optimization Problem ◽  
Unconstrained Minimization ◽  
Image Deblurring ◽  
Constrained Minimization ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Closed Form Solutions ◽  
Constrained Minimization Problem ◽  
New Variables

Image deblurring is formulated as an unconstrained minimization problem, and its penalty function is the sum of the error term and TVp-regularizers with0<p<1. Although TVp-regularizer is a powerful tool that can significantly promote the sparseness of image gradients, it is neither convex nor smooth, thus making the presented optimization problem more difficult to deal with. To solve this minimization problem efficiently, such problem is first reformulated as an equivalent constrained minimization problem by introducing new variables and new constraints. Thereafter, the split Bregman method, as a solver, splits the new constrained minimization problem into subproblems. For each subproblem, the corresponding efficient method is applied to ensure the existence of closed-form solutions. In simulated experiments, the proposed algorithm and some state-of-the-art algorithms are applied to restore three types of blurred-noisy images. The restored results show that the proposed algorithm is valid for image deblurring and is found to outperform other algorithms in experiments.

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