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The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth equations. In ...$$

Two new accelerated fixed-time stable dynamic systems are proposed for solving absolute value equations (AVEs): $Ax-|x|-b=0$. Under some mild conditions, the equilibrium point of the proposed dynamic systems is completely equivalent to the solution ...

We are focused on solving a general class of bilevel variational inequalities involving quasimonotone operators in real Hilbert spaces. A strong convergent iterative method for solving the problem is presented and analysed. Our work generalizes ...

In this paper, we first characterize generalized convex functions introduced by Linh and Penot Optimization (62: 943–959, 2013) by using generalized monotonicity of the generalized subdifferentials. We use vector variational inequalities in terms ...

In this paper, we study the sparse solution of the tensor complementarity problem (TCP), which is an NP hard problem due to the nonconvexity and noncontinuity of the ℓ 0 norm. We transform the complementarity constraints into a fixed point ...

The multi-leader–multi-follower game (MLMFG) involves two or more leaders and followers and serves as a generalization of the Stackelberg game and the single-leader–multi-follower game. Although MLMFG covers wide range of real-world applications, ...

In this paper, we use the distributionally robust approach to study stochastic variational inequalities under the ambiguity of the true probability distribution, which is referred to as distributionally robust variational inequalities (DRVIs). ...

Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution feasibility ...

This paper investigates a type of minimax linear fractional program (MLFP) that often occurs in practical problems such as design of electronic circuits, finance and investment. We first transform the MLFP problem into an equivalent problem (EP) ...

In this work, the two-stage multisplitting iteration methods based on the equivalent modulus equations are analyzed for solving linear complementarity problems. New convergence results are presented where the convergence domains of the parameter ...

• Propose two convergence theorems of the two-stage multisplitting iteration methods for LCPs with new proof techniques.
• The given results can improve the domain of the parameter matrices in the existing literatures.
• Design an ...

In this paper, we investigate bounds of solution set of the polynomial complementarity problem. When a polynomial complementarity problem has a solution, we propose a lower bound of solution norm by entries of coefficient tensors of the ...${}_{\mathrm{}}$

We consider how to solve a class of non-Lipschitz mathematical programs with equilibrium constraints (MPEC) where the objective function involves a non-Lipschitz sparsity-inducing function and other functions are smooth. Solving the non-Lipschitz ...

We present three novel algorithms based on the forward-backward splitting technique for the solution of monotone inclusion problems in real Hilbert spaces. The proposed algorithms work adaptively in the absence of the Lipschitz constant of the ...

Global approximations of scalar optimization problems in terms of variational convergence have been studied for several decades. However, there are very few results for vector models in the literature, which are limited to epi-convergence of ...

In this paper, we focus on a class of horizontal tensor complementarity problems (HTCPs). By introducing the block representative tensor, we show that finding a solution of HTCP is equivalent to finding a nonnegative solution of a related tensor ...

We first propose a new error bound for the linear complementarity problems when the involved matrices are generalized Nekrasov matrices, which generalizes the recent result obtained by Li et al. (Numer. Algorithms 74:997–1009, 2017). Then we ...

In this paper, we consider the tensor complementarity problem (TCP). From the perspective of non-coupled equality constraint minimization problem for the symmetric TCP, we propose a generalized alternating direction method of multipliers (G-ADMM) ...$\frac{\mathrm{}}{}$

By using a constant step-size, the convergence analysis of the gradient projection method on the sphere is presented for a closed spherically convex set. This algorithm is applied to discuss copositivity of operators with respect to cones. This ...

In this paper, we introduce some constants with the tensors of special structures and present their some useful properties. Furthermore, some perturbation bounds of the tensor complementarity problem are obtained on the base of these constants.

Some global error bounds with undetermined parameters, which are not always valid, for the extended vertical linear complementarity problems (LCP) of CKV-type matrices and CKV-type $B$-matrices, are presented by Yan and Wang (Jpn. J. Ind. Appl. ...$$