Variance Amplification of Accelerated First-Order Algorithms for Strongly Convex Quadratic Optimization Problems

2018 ◽  
Author(s):  
Hesameddin Mohammadi ◽  
Meisam Razaviyayn ◽  
Mihailo R. Jovanovic
Keyword(s):  
Optimization Problems ◽  
Quadratic Optimization ◽  
First Order ◽  
Convex Quadratic Optimization ◽  
Strongly Convex

scholarly journals Some remarks on duality and optimality of a class of constrained convex quadratic minimization problems

2017 ◽  
Vol 27 (2) ◽  
pp. 219-225
Author(s):  
Sudipta Roy ◽  
Sandip Chatterjee ◽  
R.N. Mukherjee
Keyword(s):  
Optimality Condition ◽  
Optimization Problems ◽  
Quadratic Optimization ◽  
Global Optimality ◽  
Convex Quadratic Optimization ◽  
Quadratic Minimization ◽  
Minimization Problems ◽  
Global Optimality Condition

In this paper the duality and optimality of a class of constrained convex quadratic optimization problems have been studied. Furthermore, the global optimality condition of a class of interval quadratic minimization problems has also been discussed.

scholarly journals From differential equation solvers to accelerated first-order methods for convex optimization

2021 ◽  
Author(s):  
Hao Luo ◽  
Long Chen
Keyword(s):  
Differential Equation ◽  
Lyapunov Function ◽  
Convex Optimization ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Point Of View ◽  
First Order ◽  
Strongly Convex ◽  
Accelerated Gradient ◽  
First Order Methods

AbstractConvergence analysis of accelerated first-order methods for convex optimization problems are developed from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient (NAG) flow, is derived from the connection between acceleration mechanism and A-stability of ODE solvers, and the exponential decay of a tailored Lyapunov function along with the solution trajectory is proved. Numerical discretizations of NAG flow are then considered and convergence rates are established via a discrete Lyapunov function. The proposed differential equation solver approach can not only cover existing accelerated methods, such as FISTA, Güler’s proximal algorithm and Nesterov’s accelerated gradient method, but also produce new algorithms for composite convex optimization that possess accelerated convergence rates. Both the convex and the strongly convex cases are handled in a unified way in our approach.

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