Search Direction Correction with Normalized Gradient Makes First-Order Methods Faster

2021 ◽  
Vol 43 (5) ◽  
pp. A3184-A3211
Author(s):  
Yifei Wang ◽  
Zeyu Jia ◽  
Zaiwen Wen
Author(s):  
Jacob Stegenga

Medical scientists employ ‘quality assessment tools’ to assess evidence from medical research, especially from randomized trials. These tools are designed to take into account methodological details of studies, including randomization, subject allocation concealment, and other features of studies deemed relevant to minimizing bias. There are dozens of such tools available. They differ widely from each other, and empirical studies show that they have low inter-rater reliability and low inter-tool reliability. This is an instance of a more general problem called here the underdetermination of evidential significance. Disagreements about the quality of evidence can be due to different—but in principle equally good—weightings of the methodological features that constitute quality assessment tools. Thus, the malleability of empirical research in medicine is deep: in addition to the malleability of first-order empirical methods, such as randomized trials, there is malleability in the tools used to evaluate first-order methods.


2020 ◽  
Vol 108 (11) ◽  
pp. 1869-1889
Author(s):  
Ran Xin ◽  
Shi Pu ◽  
Angelia Nedic ◽  
Usman A. Khan

2013 ◽  
Vol 146 (1-2) ◽  
pp. 37-75 ◽  
Author(s):  
Olivier Devolder ◽  
François Glineur ◽  
Yurii Nesterov

Author(s):  
Vasily I. Repnikov ◽  
Boris V. Faleichik ◽  
Andrew V. Moisa

In this work we present explicit Adams-type multi-step methods with extended stability intervals, which are analogous to the stabilised Chebyshev Runge – Kutta methods. It is proved that for any k ≥ 1 there exists an explicit k-step Adams-type method of order one with stability interval of length 2k. The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In the general case, to construct a k-step method of order p it is necessary to solve a constrained optimisation problem in which the objective function and p constraints are second degree polynomials in k variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability of the methods.


Author(s):  
Pavel Dvurechensky ◽  
Shimrit Shtern ◽  
Mathias Staudigl

Author(s):  
S. V. Denisov ◽  
V. V. Semenov

The problems of optimization of linear distributed systems with generalized control and first-order methods for their solution are considered. The main focus is on proving the convergence of methods. It is assumed that the operator describing the model satisfies a priori estimates in negative norms. For control problems with convex and preconvex admissible sets, the convergence of several first-order algorithms with errors in iterative subproblems is proved.


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