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[CT057]

CT057 (1/1) : Applications of dynamical systems (37N) / Mathematical programming (90C) / Higher-dimensional potential theory (31B)

Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
Type : Contributed Talk
Abstract : The original Leader-Follower (LF) model partitions all agents whose opinion is a number in $[-1,1]$ to a follower group, a leader group with a positive target opinion in $[0,1]$ and a leader group with a negative target opinion in $[-1,0]$. A leader group agent has a constant degree to its target and mixes it with the average opinion of its group neighbors at each update. A follower has a constant degree to the average opinion of the opinion neighbors of each leader group and mixes it with the average opinion of its group neighbors at each update. In this paper, we consider a variant of the LF model, namely the mixed model, in which the degrees can vary over time, the opinions can be high dimensional, and the number of leader groups can be more than two. We investigate circumstances under which all agents achieve a consensus. In particular, a few leaders can dominate the whole population.
Classification : 37N99, 05C50, 91C20, 93D50, 94C15
Format : Talk at Waseda University
Author(s) :
- Hsin-Lun Li (National Sun Yat-Sen university )
- Hsin-Lun Li (National Sun Yat-Sen university )

Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
Type : Contributed Talk
Abstract : In this talk, we present a novel stochastic normal map-based algorithm (nor-SGD) for nonconvex composite-type optimization problems and discuss its asymptotic convergence properties. We first analyze the global convergence behavior of nor-SGD and show that every accumulation point of the generated sequence of iterates is a stationary point almost surely and in an expectation sense. The obtained results hold under standard assumptions and extend the more limited convergence guarantees of nonconvex prox-SGD. In addition, based on the Kurdyka-Lojasiewicz (KL) framework and utilizing an adaptive time window mechanism, we establish almost sure convergence of the iterates and derive convergence rates that depend on the KL exponent and the step size dynamics. The techniques studied in this work can be potentially applied to other families of stochastic and simulation-based algorithms.
Classification : 90C06, 90C15, 90C26
Format : Talk at Waseda University
Author(s) :
- Andre Milzarek (The Chinese University of Hong Kong, Shenzhen)
- Junwen Qiu (The Chinese University of Hong Kong, Shenzhen)

Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
Type : Contributed Talk
Abstract : This paper presents a general framework to set the learning rate adaptively for first-order optimization methods with momentum, motivated by the derivation of Polyak step size. It is shown that the resulting methods are much less sensitive to the choice of momentum parameter and may avoid the oscillation of the heavy-ball method on ill-conditioned problems. These adaptive step sizes are further extended to the stochastic settings, which are attractive choices for stochastic gradient descent with momentum. Our methods are demonstrated to be more effective for stochastic gradient methods than prior adaptive step size algorithms in large-scale machine learning tasks.
Classification : 90C15, 65K05, 90C06
Format : Online Talk on Zoom
Author(s) :
- Xiaoyu Wang (Hong Kong University of Science and Technology)
- Mikael Johansson (KTH Royal Institute of Technology)
- Tong Zhang (Hong Kong University of Science and Technology)

Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
Type : Contributed Talk
Abstract : Nonconvex sparse optimization problems with the trimmed l1 norm or truncated nuclear norm, which is a penalty function of cardinality or rank constraint, have been actively studied. A unified framework that includes all the existing trimmed l1-penalized problems is introduced. We show that under mild conditions, any d-stationary point of the penalized problem satisfies the corresponding constraint. Our result is superior to almost all existing results, especially from the viewpoint of practice.
Classification : 90C06, 90C26, 90C30, 90C46, 90C90
Author(s) :
- Shotaro Yagishita (Chuo University)
- Jun-ya Gotoh (Chuo University)

Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
Type : Contributed Talk
Abstract : The boundary domain integral equation method is an important tool to formulate (in terms of integral operators) boundary value problems with variable coefficients. Although the theory of boundary domain integral equations has been largely developed, there is a lack of results in numerical implementations. The aim of this talk is to enumerate the different boundary domain formulations for several boundary conditions and present discretizations of the integral equation systems and comparisons between the numerical behavior of the approximated solutions.
Classification : 31B10, 65Rxx, boundary domain integral methods
Author(s) :
- Nahuel Domingo Caruso (National University of Rosario - CIFASIS-CONICET)
- Carlos Fresneda-Portillo (Universidad Loyola Andalucía (Spain))