Novel self-adaptive algorithms for non-Lipschitz equilibrium problems with applications

Anh, Pham Ky; Hai, Trinh Ngoc

doi:10.1007/s10898-018-0722-2

Cited by 9 publications

(2 citation statements)

References 28 publications

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“…✷ One advantage of Algorithm 2 is that it can be applied to find a solution of nonmonotone and Lipschitz-type equilibrium problems without using linesearch rules to determine the step size. However, this step size is proportional to 1 L (L = max{L 1 , L 2 }), so when the Lipschitz constants of f are large, the step size is small. This leads to the algorithm can be slow.…”

Section: ) Having X K Do the Following Stepsmentioning

confidence: 99%

“…These methods often require the convexity on the second variable and the monotonicity or generalized monotonicity of the bifunction f . Up to now, several results have been achieved for this class of equilibrium problems (see papers [1,13,22,29,32] and books [2,16]). Recently, J. Strodiot et al in [28] (see also [7,9,15]) have introduced shrinking projection algorithms to solve nonmonotone equilibrium problems.…”

Section: Introductionmentioning

confidence: 99%

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A novel method for solving nonmonotone equilibrium problems

Huyen,

Duc,

Thanh

et al. 2023

Preprint

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In this paper, we propose a novel projection method for finding a solution of equilibrium problems EP($C, f$) in Euclidean spaces in which the bifunction does not require to be satisfied any monotonicity. Unlike methods for solving such a problem used in the literature, shrinking projection methods which may raise cost of computation, we suggest using an adaptive projection method incorporate with linesearch procedures to solve these problems when the bifunction does not satisfy the Lipschitz type condition. These linesearches are unnecessary when $f$ satisfies the Lipschitz type condition with constants $L_1$ and $L_2$. In case these constants are unknown, we propose to use the adaptive step sizes. All algorithms are proven to converge to a solution of the considered problem, and some numerical examples are also reported to illustrate the efficiency of the proposed algorithms. Mathematics Subject Classification (2000) 90C26 · 90C33 · 47J20 · 65K15 · 65J20

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Section: ) Having X K Do the Following Stepsmentioning

confidence: 99%