ON THE MONOTONE CONVERGENCE OF THE PROJECTED ITERATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.

MONOTONE ITERATION FOR ELLIPTIC PDEs WITH DISCONTINUOUS NONLINEAR TERMS

In this paper, we use monotone iterative techniques to show the existence of maximal or minimal solutions of some elliptic PDEs with nonlinear discontinuous terms. As the numerical analysis of this PDEs is concerned, we prove the convergence of discrete extremal solutions.

Iterative Solution for Systems of Binary Non-mixed Monotone Operator Equations

With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized.

Monotone Iterative Method for Nonlinear Discontinuous Differential Equations

A monotone iterative method for some discontinuous variational boundary problems is given, the convergence of iterative solutions is proved by the theory of partially ordered sets. It can be regarded as a generalization of the classical monotone iteration theory for continuous problems.

ON MONOTONE ITERATIVE METHOD FOR INITIAL VALUE PROBLEMS OF NONLINEAR SECOND-ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.

SOME NEW ITERATIVE ALGORITHMS FOR MONOTONE MIXED VARIATIONAL INEQUALITIES

In this paper,some new iterative algorithms for monotone mixed variational inequalities and the convergence in real Hilbert spaces are studied.

Monotone Iterative Methodfor Nonlinear Discontinuous ParabolicDifferential Equations

In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.

AN ITERATIVE ALGORITHM FOR MAXIMAL MONOTONE MULTIVALUED OPERATOR EQUATIONS

A proximal iterative algorithm for the mulitivalue operator equation 0 ∈ T(x) is presented, where T is a maximal monotone operator. It is an improvement of the proximal point algorithm as well know. The convergence of the algorithm is discussed and all example is given.

The Iterative Solution for a Class of Monotone Operator Equations

The iterative solution for a class of multivalued monotone operator equations just like A(u)∈-B(u) is discussed, where A is a positive definite linear single valued operator, B is a bounded and monotone multivalued operator. The existence and convergence of approximate solutions are proved. The method of numerical realization is demonstrated in some examples.

Iterative Solutions for a Non-monotone BinaryOperator Equations and Operator System of Equations

By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations.

Distributed Optimal Variational GNE Seeking in Merely Monotone Games

In this paper, the optimal variational generalized Nash equilibrium(v-GNE) seeking problem in merely monotone games with linearly coupled cost functions is investigated, in which the feasible strategy domain of each agent is coupled through an affine constraint. A distributed algorithm based on the hybrid steepest descent method is first proposed to seek the optimal v-GNE. Then, an accelerated algorithm with relaxation is proposed and analyzed, which has the potential to further improve the convergence speed to the optimal v-GNE. Some sufficient conditions in both algorithms are obtained to ensure the global convergence towards the optimal v-GNE. To illustrate the performance of the algorithms, numerical simulation is conducted based on a networked Nash-Cournot game with bounded market capacities.

PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.

Fast and Accurate Predictor-Corrector Methods Using Feedback-Accelerated Picard Iteration for Strongly Nonlinear Problems

Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.

Calculation of Mass Concrete Temperature Containing Cooling Water Pipe Based on Substructure and Iteration Algorithm

Mathematical physics equations are often utilized to describe physical phenomena in various fields of science and engineering.One such equation is the Fourier equation,which is a commonly used and effective method for evaluating the effectiveness of temperature control measures for mass concrete.One important measure for temperature control in mass concrete is the use of cooling water pipes.However,the mismatch of grids between large-scale concrete models and small-scale cooling pipe models can result in a significant waste of calculation time when using the finite element method.Moreover,the temperature of the water in the cooling pipe needs to be iteratively calculated during the thermal transfer process.The substructure method can effectively solve this problem,and it has been validated by scholars.The Abaqus/Python secondary development technology provides engineers with enough flexibility to combine the substructure method with an iteration algorithm,which enables the creation of a parametric modeling calculation for cooling water pipes.This paper proposes such a method,which involves iterating the water pipe boundary and establishing the water pipe unit substructure to numerically simulate the concrete temperature field that contains a cooling water pipe.To verify the feasibility and accuracy of the proposed method,two classic numerical examples were analyzed.The results showed that this method has good applicability in cooling pipe calculations.When the value of the iteration parameterαis 0.4,the boundary temperature of the cooling water pipes can meet the accuracy requirements after 4∼5 iterations,effectively improving the computational efficiency.Overall,this approach provides a useful tool for engineers to analyze the temperature control measures accurately and efficiently for mass concrete,such as cooling water pipes,using Abaqus/Python secondary development.

Value Iteration-Based Cooperative Adaptive Optimal Control for Multi-Player Differential Games With Incomplete Information

This paper presents a novel cooperative value iteration(VI)-based adaptive dynamic programming method for multi-player differential game models with a convergence proof.The players are divided into two groups in the learning process and adapt their policies sequentially.Our method removes the dependence of admissible initial policies,which is one of the main drawbacks of the PI-based frameworks.Furthermore,this algorithm enables the players to adapt their control policies without full knowledge of others’ system parameters or control laws.The efficacy of our method is illustrated by three examples.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Another SSOR Iteration Method

Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.

Iteration and evaluation of shale oil development technology for continental rift lake basins

By benchmarking with the iteration of drilling technology,fracturing technology and well placement mode for shale oil and gas development in the United States and considering the geological characteristics and development difficulties of shale oil in the Jiyang continental rift lake basin,East China,the development technology system suitable for the geological characteristics of shale oil in continental rift lake basins has been primarily formed through innovation and iteration of the development,drilling and fracturing technologies.The technology system supports the rapid growth of shale oil production and reduces the development investment cost.By comparing it with the shale oil development technology in the United States,the prospect of the shale oil development technology iteration in continental rift lake basins is proposed.It is suggested to continuously strengthen the overall three-dimensional development,improve the precision level of engineering technology,upgrade the engineering technical indicator system,accelerate the intelligent optimization of engineering equipment,explore the application of complex structure wells,form a whole-process integrated quality management system from design to implementation,and constantly innovate the concept and technology of shale oil development,so as to promote the realization of extensive,beneficial and high-quality development of shale oil in continental rift lake basins.