The Log—Quadratic Proximal Methodology in Convex Optimization Algorithms and Variational Inequalities

2003 ◽  
pp. 19-52 ◽  
Author(s):  
Alfred Auslender ◽  
Marc Teboulle
Keyword(s):  
Convex Optimization ◽  
Variational Inequalities ◽  
Optimization Algorithms

scholarly journals Image reconstruction algorithm based on variable atomic number matching pursuit

2016 ◽  
Vol 11 (2) ◽  
pp. 103-109
Author(s):  
Hongtu Zhao ◽  
Chong Chen ◽  
Chenxu Shi
Keyword(s):  
Image Reconstruction ◽  
Convex Optimization ◽  
Atomic Number ◽  
Matching Pursuit ◽  
Greedy Algorithms ◽  
Optimization Algorithms ◽  
Reconstruction Algorithm ◽  
Reconstruction Algorithms ◽  
Reconstruction Quality ◽  
Stable Reconstruction

As the most critical part of compressive sensing theory, reconstruction algorithm has an impact on the quality and speed of image reconstruction. After studying some existing convex optimization algorithms and greedy algorithms, we find that convex optimization algorithms should possess higher complexity to achieve higher reconstruction quality. Also, fixed atomic numbers used in most greedy algorithms increase the complexity of reconstruction. In this context, we propose a novel algorithm, called variable atomic number matching pursuit, which can improve the accuracy and speed of reconstruction. Simulation results show that variable atomic number matching pursuit is a fast and stable reconstruction algorithm and better than the other reconstruction algorithms under the same conditions.

scholarly journals Active‐Set Newton Methods and Partial Smoothness

2020 ◽  
Author(s):  
Adrian S. Lewis ◽  
Calvin Wylie
Keyword(s):  
Nonlinear Programming ◽  
Variational Inequalities ◽  
Finite Time ◽  
Optimization Algorithms ◽  
Newton Methods ◽  
Active Set ◽  
Local Algorithms ◽  
Partial Smoothness ◽  
Analogous Behavior ◽  
Partly Smooth

Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to variational inequalities over partly smooth sets. As in classical nonlinear programming, such active‐set structure underlies the design of accelerated local algorithms of Newton type. We formalize this idea in broad generality as a simple linearization scheme for two intersecting manifolds.

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