scholarly journals A Fixed-Point Policy-Iteration-Type Algorithm for Symmetric Nonzero-Sum Stochastic Impulse Control Games

2020 ◽  
Author(s):  
Diego Zabaljauregui
Keyword(s):  
Fixed Point ◽  
Impulse Control ◽  
Strong Dependence ◽  
Policy Iteration ◽  
Initial Guess ◽  
Previous Method ◽  
Modelling Framework ◽  
Symmetric Games ◽  
Type Algorithm ◽  
Analytical Approaches

Abstract Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has hindered their proliferation. Semi-analytical approaches make strong assumptions pertaining to very particular cases. To the author’s best knowledge, the only numerical method in the literature is the heuristic one we put forward in Aïd et al (ESAIM Proc Surv 65:27–45, 2019) to solve an underlying system of quasi-variational inequalities. Focusing on symmetric games, this paper presents a simpler, more precise and efficient fixed-point policy-iteration-type algorithm which removes the strong dependence on the initial guess and the relaxation scheme of the previous method. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. A novel provably convergent single-player impulse control solver is also provided. The main algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise very challenging problems, and even some which go beyond the scope of the currently available theory.

scholarly journals ALGORITHMIC AND ANALYTICAL APPROACHES TO THE SPLIT FEASIBILITY PROBLEMS AND FIXED POINT PROBLEMS

2013 ◽  
Vol 17 (5) ◽  
pp. 1839-1853 ◽  
Author(s):  
Yeong-Cheng Liou ◽  
Li-Jun Zhu ◽  
Yonghong Yao ◽  
Chiuh-Cheng Chyu
Keyword(s):  
Fixed Point ◽  
Fixed Point Problems ◽  
Split Feasibility Problems ◽  
Analytical Approaches ◽  
Split Feasibility

scholarly journals Inertial Mann-Type Algorithm for a Nonexpansive Mapping to Solve Monotone Inclusion and Image Restoration Problems

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 750
Author(s):  
Natthaphon Artsawang ◽  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Image Restoration ◽  
Zero Point ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Type Method ◽  
Type Algorithm ◽  
Inertial Terms

In this article, we establish a new Mann-type method combining both inertial terms and errors to find a fixed point of a nonexpansive mapping in a Hilbert space. We show strong convergence of the iterate under some appropriate assumptions in order to find a solution to an investigative fixed point problem. For the virtue of the main theorem, it can be applied to an approximately zero point of the sum of three monotone operators. We compare the convergent performance of our proposed method, the Mann-type algorithm without both inertial terms and errors, and the Halpern-type algorithm in convex minimization problem with the constraint of a non-zero asymmetric linear transformation. Finally, we illustrate the functionality of the algorithm through numerical experiments addressing image restoration problems.

scholarly journals Measuring Equity Across the Nordic Education Systems—Conceptual and Methodological Choices as Implications for Educational Policies

2020 ◽  
pp. 43-71
Author(s):  
Oleksandra Mittal ◽  
Trude Nilsen ◽  
Julius K. Björnsson
Keyword(s):  
Structural Equation ◽  
Educational Equity ◽  
Research Process ◽  
Nordic Countries ◽  
Bivariate Analysis ◽  
Modelling Framework ◽  
Eighth Grade Students ◽  
Status Measure ◽  
Education Decision ◽  
Analytical Approaches

AbstractEver since international large-scale student assessments made it possible to rank countries according to their equitability, Nordic countries have topped these rankings. Nevertheless, a decline in equity has been reported lately. However, the process of empirical enquiry that leads to specific inferences on equity partly stays obscure to education decision-makers. This unawareness of the boundaries of specific methodological and analytical approaches may lead to wrong interpretations and policy implications. Therefore, our aim is to discuss and empirically illustrate how the array of choices taken throughout the research process, from equity conceptualization and operationalization to its measurement, may affect the inferences on educational equity for Nordic countries. Our sample includes fourth- and eighth-grade students from Norway, Sweden, Denmark and Finland who participated in TIMSS 2015. We applied two-level multigroup regression models within the structural equation modelling framework to investigate the sensitivity of the countries’ level of equity to: (a) operationalization of the socioeconomic status measure; (b) operationalization of equity or, in other words, the method of analysis employed (e.g., bivariate analysis versus univariate); (c) single-level against multilevel analytical approaches; (d) the grade/age of students; and (e) the choice of the learning outcome across subject domains. Prior to the analyses, we estimated the comparability of SES as a latent construct between Nordic countries. Our results confirmed that some of the most common choices to measure educational equity do matter. Thus, we would encourage a researcher to report elaborately on the research process and inform on its limitations because if interpreted wrongly, it may have unfavourable consequences for a particular group of individuals.

scholarly journals Weakly Chained Matrices, Policy Iteration, and Impulse Control

2016 ◽  
Vol 54 (3) ◽  
pp. 1341-1364 ◽  
Author(s):  
P. Azimzadeh ◽  
P. A. Forsyth
Keyword(s):  
Impulse Control ◽  
Policy Iteration

scholarly journals Viscosity Methods and Split Common Fixed Point Problems for Demicontractive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 844 ◽  
Author(s):  
Yaqin Wang ◽  
Xiaoli Fang ◽  
Tae-Hwa Kim
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
A Priori ◽  
Fixed Point Problems ◽  
A Priori Knowledge ◽  
Type Algorithm ◽  
Operator Norms ◽  
Demicontractive Mappings ◽  
Split Common Fixed Point

We, first, propose a new method for solving split common fixed point problems for demicontractive mappings in Hilbert spaces, and then establish the strong convergence of such an algorithm, which extends the Halpern type algorithm studied by Wang and Xu to a viscosity iteration. Above all, the step sizes in this algorithm are chosen without a priori knowledge of the operator norms.

scholarly journals A General Inertial Projection-Type Algorithm for Solving Equilibrium Problem in Hilbert Spaces with Applications in Fixed-Point Problems

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 101 ◽  
Author(s):  
Nopparat Wairojjana ◽  
Habib ur Rehman ◽  
Manuel De la Sen ◽  
Nuttapol Pakkaranang
Keyword(s):  
Fixed Point ◽  
Mathematical Programming ◽  
Hilbert Spaces ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Type Condition ◽  
Variable Stepsize ◽  
Mild Conditions ◽  
Strict Pseudocontraction ◽  
Type Algorithm

A plethora of applications from mathematical programming, such as minimax, and mathematical programming, penalization, fixed point to mention a few can be framed as equilibrium problems. Most of the techniques for solving such problems involve iterative methods that is why, in this paper, we introduced a new extragradient-like method to solve equilibrium problems in real Hilbert spaces with a Lipschitz-type condition on a bifunction. The advantage of a method is a variable stepsize formula that is updated on each iteration based on the previous iterations. The method also operates without the previous information of the Lipschitz-type constants. The weak convergence of the method is established by taking mild conditions on a bifunction. For application, fixed-point theorems that involve strict pseudocontraction and results for pseudomonotone variational inequalities are studied. We have reported various numerical results to show the numerical behaviour of the proposed method and correlate it with existing ones.

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