Nonsmooth analysis approach to Isaac's equation [PDF]
International Journal of Mathematics and Mathematical Sciences, 1993 We study Isaacs' equation (∗)wt(t,x)+H(t,x,wx(t,x))=0 (H is a highly nonlinear function) whose natural solution is a value W(t,x) of a suitable differential game.
Leszek S. Zaremba
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Linearized ADMM for Nonconvex Nonsmooth Optimization With Convergence Analysis [PDF]
IEEE Access, 2019 Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine learning, communications, and many other fields.
Qinghua Liu, Xinyue Shen, Yuantao Gu
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Nonsmooth analysis of three-dimensional slipping and rolling in the presence of dry friction. [PDF]
Nonlinear Dyn, 2019 In this paper, the nonsmooth dynamics of two contacting rigid bodies is analysed in the presence of dry friction. In three dimensions, slipping can occur in continuously many directions.
Antali M, Stepan G.
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Truncated nonsmooth Newton multigrid for phase-field brittle-fracture problems, with analysis [PDF]
Computational Mechanics, 2023 We propose the truncated nonsmooth Newton multigrid method (TNNMG) as a solver for the spatial problems of the small-strain brittle-fracture phase-field equations.
Carsten Gräser +2 more
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An Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth Data [PDF]
SIAM Journal on Numerical Analysis, 2018 We introduce a modified L1 scheme for solving time fractional partial differential equations and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and inhomogeneous cases. Jin, Lazarov, and Zhou [IMA J. Numer.
Yubin Yan +2 more
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Convergence Analysis of a Petrov–Galerkin Method for Fractional Wave Problems with Nonsmooth Data [PDF]
Journal of Scientific Computing, 2019 This paper analyzes the convergence of a Petrov–Galerkin method for time fractional wave problems with nonsmooth data. Well-posedness and regularity of the weak solution to the time fractional wave problem are firstly established.
Hao Luo, Binjie Li, Xiaoping Xie
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Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold [PDF]
Journal of Differential Equations, 2018 We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family.
Bastos, Jéfferson L. R. +3 more
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A Unified Convergence Analysis of Block Successive Minimization Methods for Nonsmooth Optimization [PDF]
SIAM Journal on Optimization, 2012 The block coordinate descent (BCD) method is widely used for minimizing a continuous function $f$ of several block variables. At each iteration of this method, a single block of variables is optimized, while the remaining variables are held fixed.
Meisam Razaviyayn +2 more
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Analysis of Limited-Memory BFGS on a Class of Nonsmooth Convex Functions [PDF]
IMA Journal of Numerical Analysis, 2018 The limited-memory BFGS (Broyden-Fletcher-Goldfarb-Shanno) method is widely used for large-scale unconstrained optimization, but its behavior on nonsmooth problems has received little attention. L-BFGS (limited memory BFGS) can be used with or without ‘
A Nasrollah Zadeh Asl +1 more
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Distributed Continuous-Time Algorithm for Constrained Convex Optimizations via Nonsmooth Analysis Approach [PDF]
IEEE Transactions on Automatic Control, 2015 This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its local cost ...
Xianlin Zeng, Peng Yi, Yiguang Hong
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