Finite Iteration Research Articles

Probability matching and strategic decision making

This paper examines a link between an individual’s (possibly limited) strategic thinking in the 11–20 money request game and (possibly non-rational) decision-making patterns in the matching pennies games. Experimental evidence shows that subjects’ strategic behavior, which used to be understood as a result of finite cognitive iterations, is closely related to their choice randomization patterns. Ignoring some individuals’ choice randomization may bias the population variance of levels in cognitive iterations. Choice randomizers, which we call probability matchers, are non-rational in both the non-strategic and strategic settings, but their choice patterns are systematic—although inconsistent with rational decisions—and similar.

Stochastic event-based LQG control: An analysis on strict consistency

This paper studies the discrete-time linear–quadratic-Gaussian problem under partial-information-based sensors and event-based transmissions. By constructing a special form of stochastic event-based protocols, the optimal control policy is obtained, which minimizes an average quadratic cost function under a fixed transmission protocol. Then, analytical expressions of the corresponding transmission and control performance are derived. To evaluate the efficiency of event-based protocols, the concept of strict consistency is introduced, which requires that the control performance of event-based protocols be strictly better than that of the periodic protocol under the same transmission rate. Based on the obtained analytical expressions, the strict consistency is proved by showing that the periodic protocol corresponds to a local maximum point in the design space of parameters. To further improve the control performance of stochastic event-based protocols, an iterative parameter design algorithm (with finite iterations) is proposed for ensuring a strict reduction in cost functions after each iteration. Finally, numerical simulations are provided to illustrate the theoretical results.

Towards Automatic Deductive Verification of C Programs with Sisal Loops Using the C-lightVer System

The C-lightVer system is developed in IIS SB RAS for C-program deductive verification. C-kernel is an intermediate verification language in this system. Cloud parallel programming system (CPPS) is also developed in IIS SB RAS. Cloud Sisal is an input language of CPPS. The main feature of CPPS is implicit parallel execution based on automatic parallelization of Cloud Sisal loops. Cloud-Sisal-kernel is an intermediate verification language in the CPPS system. Our goal is automatic parallelization of such a superset of C that allows implementing automatic verification. Our solution is such a superset of C-kernel as C-Sisal-kernel. The first result presented in this paper is an extension of C-kernel by Cloud-Sisal-kernel loops. We have obtained the C-Sisal-kernel language. The second result is an extension of C-kernel axiomatic semantics by inference rule for Cloud-Sisal-kernel loops. The paper also presents our approach to the problem of deductive verification automation in the case of finite iterations over data structures. This kind of loops is referred to as definite iterations. Our solution is a composition of symbolic method of verification of definite iterations, verification condition metageneration and mixed axiomatic semantics method. Symbolic method of verification of definite iterations allows defining inference rules for these loops without invariants. Symbolic replacement of definite iterations by recursive functions is the base of this method. Obtained verification conditions with applications of recursive functions correspond to logical base of ACL2 prover. We use ACL2 system based on computable recursive functions. Verification condition metageneration allows simplifying implementation of new inference rules in a verification system. The use of mixed axiomatic semantics results to simpler verification conditions in some cases.

INVESTIGATION OF THERMO-HYDRAULIC PERFORMANCE OF NANOFLUIDS IN A ZIGZAG CHANNEL WITH BAFFLES

In this study, the thermo-hydraulic performance of Al2O3-water nanofluid in a zigzag channel with baffles were numerically investigated. The mass, momentum and energy equations are discretized with finite volume approach and iterations are solved with SIMPLE algorithm. Reynolds number (200 ≤ Re ≤ 1600), and nanoparticle volume fraction (0.01 ≤ φ ≤ 0.03) were changed, and other parameters kept constant. The lower and upper zigzag surfaces of the channel were kept at constant temperature, and the Nusselt number and friction factor along the channel were calculated. The velocity and temperature contours in the channel were obtained in order to observe the effects on flow and heat transfer of the paramerers. The results shown that the increasing particle volume fractions and Reynolds numbers improved the heat transfer, while the friction factor increased slightly. The best thermo-hydraulic performance was obtained at Re = 1400 and φ = 3% as approximately 1.15.

On properties of one functional used in software constructions for solving differential games

Nonlinear differential game (DG) is investigated; relaxations of the game problem of guidance are investigated also. The variant of the program iterations method realized in the space of position functions and delivering in limit the value function of the minimax-maximin DG for special functionals of a trajectory is considered. For every game position, this limit function realizes the least size of the target set neighborhood for which, under proportional weakening of phase constraints, the player interested in a guidance yet guarantees its realization. Properties of above-mentioned functionals and limit function are investigated. In particular, sufficient conditions for realization of values of given function under fulfilment of finite iteration number are obtained.

Preservation of splitting families and cardinal characteristics of the continuum

We show how to construct, via forcing, splitting families that are preserved by a certain type of finite support iterations. As an application, we construct a model where 15 classical characteristics of the continuum are pairwise different, concretely: the 10 (non-dependent) entries in Cichoń’s diagram, mathfrak{m} (2-Knaster), mathfrak{p}, mathfrak{h}, the splitting number mathfrak{s} and the reaping number mathfrak{r}.

Algorithmically-consistent deep learning frameworks for structural topology optimization

Topology optimization has emerged as a popular approach to refine a component’s design and increase its performance. However, current state-of-the-art topology optimization frameworks are compute-intensive, mainly due to multiple finite element analysis iterations required to evaluate the component’s performance during the optimization process. Recently, machine learning (ML)-based topology optimization methods have been explored by researchers to alleviate this issue. However, previous ML approaches have mainly been demonstrated on simple two-dimensional applications with low-resolution geometry. Further, current methods are based on a single ML model for end-to-end prediction, which requires a large dataset for training. These challenges make it non-trivial to extend current approaches to higher resolutions. In this paper, we develop deep learning-based frameworks consistent with traditional topology optimization algorithms for 3D topology optimization with a reasonably fine (high) resolution. We achieve this by training multiple networks, each learning a different step of the overall topology optimization methodology, making the framework more consistent with the topology optimization algorithm. We demonstrate the application of our framework on both 2D and 3D geometries. The results show that our approach predicts the final optimized design better (5.76× reduction in total compliance MSE in 2D; 2.03× reduction in total compliance MSE in 3D) than current ML-based topology optimization methods.

An iterative algorithm for generalized Hamiltonian solution of a class of generalized coupled Sylvester-conjugate matrix equations

In this work, we present an iterative algorithm to solve a class of generalized coupled Sylvester-conjugate matrix equations over the generalized Hamiltonian matrices. We show that if the equations are consistent, a generalized Hamiltonian solution can be obtained within finite iteration steps in the absence of round-off errors for any initial generalized Hamiltonian matrix by the proposed iterative algorithm. Furthermore, we can obtain the minimum-norm generalized Hamiltonian solution by choosing the special initial matrices. Finally, numerical examples show that the iterative algorithm is effective.

A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam

The accurate description of the flow of water in porous media is of the greatest importance due to its numerous applications in several areas (groundwater, soil mechanics, etc.). The nonlinear Richards equation is often used as the governing equation that describes this phenomenon and a large number of research studies aimed to solve it numerically. However, due to the nonlinearity of the constitutive expressions for permeability, it remains a challenging modeling problem. In this paper, the stationary form of Richards’ equation used in saturated soils is solved by two numerical methods: generalized finite differences, an emerging method that has been successfully applied to the transient case, and a finite element method, for benchmarking. The nonlinearity of the solution in both cases is handled using a Newtonian iteration. The comparative results show that a generalized finite difference iteration yields satisfactory results in a standard test problem with a singularity at the boundary.

Developing iterative algorithms to solve Sylvester tensor equations

This paper is concerned with solving high order Sylvester tensor equation arising in control theory. We propose the tensor forms of the bi-conjugate gradient and bi-conjugate residual methods for solving the tensor equation. To improve their performance, two preconditioned iterative algorithms based on the nearest Kronecker product are developed for finding its solution. We also prove that the proposed algorithms are convergent to an exact solution within finite iteration steps for any initial tensor in the absence of round-off errors. At last, some numerical examples are provided to illustrate the feasibility and validity of the algorithms proposed.

Task offloading and resource allocation algorithm based on mobile edge computing in Internet of Things environment

This paper proposes a task offloading and resource allocation algorithm based on mobile edge computing. Firstly, for the long-term performance optimization of small base stations, the system model is established according to task arrival characteristics, credit relationship between small base stations, time delay and energy consumption of computing tasks and cable channel congestion. Secondly, the energy consumption deficit queue based on Lyapunov drift penalty technology used for the energy consumption constraint of small base stations in long-term optimization process. The energy consumption deficit queue is established for each small base station to couple the energy consumption and time of small base stations, so that small base stations can meet the energy consumption constraints in long-term optimization process. Finally, game theory is introduced to calculate offloading weight by the offloading weight model based on Shapley value. Besides, the offloading weight is calculated equitably according to the return of different tasks. Simulation results on MATLAB platform show that the proposed algorithm can achieve Nash equilibrium after finite iterations. Moreover, its performance on energy consumption, time delay and number of tasks successfully offloaded is better than other comparison strategies.

Wasserstein Distributionally Robust Inverse Multiobjective Optimization

Inverse multiobjective optimization provides a general framework for the unsupervised learning task of inferring parameters of a multiobjective decision making problem (DMP), based on a set of observed decisions from the human expert. However, the performance of this framework relies critically on the availability of an accurate DMP, sufficient decisions of high quality, and a parameter space that contains enough information about the DMP. To hedge against the uncertainties in the hypothetical DMP, the data, and the parameter space, we investigate in this paper the distributionally robust approach for inverse multiobjective optimization. Specifically, we leverage the Wasserstein metric to construct a ball centered at the empirical distribution of these decisions. We then formulate a Wasserstein distributionally robust inverse multiobjective optimization problem (WRO-IMOP) that minimizes a worst-case expected loss function, where the worst case is taken over all distributions in the Wasserstein ball. We show that the excess risk of the WRO-IMOP estimator has a sub-linear convergence rate. Furthermore, we propose the semi-infinite reformulations of the WRO-IMOP and develop a cutting-plane algorithm that converges to an approximate solution in finite iterations. Finally, we demonstrate the effectiveness of our method on both a synthetic multiobjective quadratic program and a real world portfolio optimization problem.

An iterative algorithm for generalized periodic multiple coupled Sylvester matrix equations

The paper is indicated to constructing a modified conjugate gradient iterative (MCG) algorithm to solve the generalized periodic multiple coupled Sylvester matrix equations. It can be proved that the proposed approach can find the solution within finite iteration steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrices to obtain the least Frobenius norm solution of the system. Some numerical examples are illustrated to show the performance of the proposed approach and its superiority over the existing method CG.

A posteriori error analysis for Schwarz overlapping domain decomposition methods

Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive overlapping Schwarz domain decomposition methods. The numerical error in a user-specified functional of the solution (quantity of interest) is decomposed into contributions that arise as a result of the finite iteration between the subdomains and from the spatial discretization. The spatial discretization contribution is further decomposed into contributions arising from each subdomain. This decomposition of the numerical error is used to construct a two stage solution strategy that efficiently reduces the error in the quantity of interest by adjusting the relative contributions to the error.

GSDAR: a fast Newton algorithm for $$\ell _0$$ regularized generalized linear models with statistical guarantee

We propose a fast Newton algorithm for $$\ell _0$$ regularized high-dimensional generalized linear models based on support detection and root finding. We refer to the proposed method as GSDAR. GSDAR is developed based on the KKT conditions for $$\ell _0$$ -penalized maximum likelihood estimators and generates a sequence of solutions of the KKT system iteratively. We show that GSDAR can be equivalently formulated as a generalized Newton algorithm. Under a restricted invertibility condition on the likelihood function and a sparsity condition on the regression coefficient, we establish an explicit upper bound on the estimation errors of the solution sequence generated by GSDAR in supremum norm and show that it achieves the optimal order in finite iterations with high probability. Moreover, we show that the oracle estimator can be recovered with high probability if the target signal is above the detectable level. These results directly concern the solution sequence generated from the GSDAR algorithm, instead of a theoretically defined global solution. We conduct simulations and real data analysis to illustrate the effectiveness of the proposed method.

On ductile fracture of 30CrMnSiNi2A steel considering effects of stress triaxiality

30CrMnSiNi2A steel is a high-strength low-alloy steel and it is widely used in the defense industry. Its ductile fracture properties were investigated by using a combined experimental-numerical approach to address the need for assessment of structural integrity. The parameters of the Johnson-Cook constitutive model were obtained through quasi-static and dynamic tensile tests on round bar specimens at different temperatures and relevant finite element method iterations. The effects of strain rate and temperature on fracture were studied. The tensile tests on notched round bar specimens were performed to calibrate the fracture strain in the range of high positive stress triaxiality. The tensile tests on butterfly plates and compression tests on short cylindrical specimens covered the fracture properties in the range of low and negative stress triaxiality. The finite element models were computed and the fracture loci in the space of the effective plastic strain to fracture and the stress triaxiality in a wide range from −1/3 to 1.5 were constructed. The parameters of the Johnson-Cook fracture model and Bao-Wierzbicki fracture model were calibrated. It is shown that stress triaxiality has a significant effect on the fracture of 30CrMnSiNi2A steel and the monotonicity of the fracture loci varies in different stress triaxiality range. The Bao-Wierzbicki model is capable of predicting the fracture patterns of the 30CrMnSiNi2A steel in different stress states.

Dynamic optimization of nonlinear systems with guaranteed feasibility of inequality-path-constraints

An algorithm is proposed for locating an optimal solution satisfying the KKT conditions to a specified tolerance to inequality-path-constrained dynamic optimization (PCDO) problem within finite iterations. This algorithm solves the optimization problem by iteratively approximating the original optimization problem through adaptive convexification of its lower level programs. In the process of convexification of the lower level programs, αBB technique is used adaptively to construct convex relaxations of a path constraint in each time subinterval. Compared to the result in (Fu, Faust, Chachuat, & Mitsos, 2015), the distinguishing feature is that the proposed algorithm avoids numerically solving the non-convex lower level program to global optimality at each iteration. Two numerical examples are shown to demonstrate the performance of the algorithm.

Constitutive equation of compacted graphite iron (GJV450) at high temperature and high strain rate

Compacted graphite iron (CGI) is an ideal material for the cylinder block and cylinder head of diesel engine because of its excellent physical and mechanical properties. At present, the researches on CGI mainly focused on experimental study of machining CGI, there are few studies on the cutting simulation of CGI, especially the high-speed machining simulation of CGI, and the constitutive equation of CGI at high temperature and high strain rate has not been studied. In this paper, the stress-strain relationship under quasi-static condition was obtained by quasi-static tensile test, and the power law constitutive equation of CGI with a grade of GJV450 under the condition of large strain, high strain rate, and high temperature was built by orthogonal cutting experiments and finite element iteration. The established power law constitutive equation was applied to the finite element simulation of the cutting process of CGI, which improves the accuracy of finite element analysis. The chip morphology of CGI and the distribution of plastic strain and temperature in the cutting process were analyzed by finite element simulation.

Finite‐time distributed block‐decomposed information filter for nonlinear systems with colored measurement noise

AbstractThis paper considers the distributed filtering problem for discrete‐time nonlinear systems with colored measurement noise obeying a nonlinear autoregressive process in sensor networks. A novel block‐decomposed information‐type filter for such systems is proposed in a centralized fusion structure, by using the statistical linear regression to deal with model nonlinearities and the measurement difference approach to overcome the noise correlation caused by colored measurement noises. Meanwhile, with the help of block matrix inverse operation to realize the high‐dimensional block matrix decomposition, the information vector and information matrix of the original system state in the designed information filter is directly estimated recursively, so as to own good numerical stability. Then, the finite‐time distributed implementation of the proposed filter is put forward, where the final filtering estimate in each sensor node is consistent with the centralized filtering result, by ensuring that each sensor node directly obtains the average values of shared variables in the sensor network through finite iterations of average consensus. Finally, the posterior Cramér–Rao lower bound is derived to show the proposed filter reaches the optimal theoretical performance bound in the premise of statistical linear regression and Gaussian posterior probability density approximation. A target tracking example with colored measurement noise obeying a linear and a nonlinear autoregressive processes validates the proposed method.

Optimization of Frequency Selective Surfaces for the Design of Electromagnetic Mantle Cloaks

A full optimization procedure that combines the parallel self-adaptive low-high evaluation-evolutionary algorithm with the finite element method-robin boundary condition iteration numerical method is proposed for the design of electromagnetic mantle cloaks enclosing arbitrary objects. The procedure is efficiently applied to optimize an ultrathin, conformal frequency selective surface (FSS), placed around an inhomogeneous dielectric cylinder to be made invisible. Two very different optimal solutions have been found, and this can be a great advantage for the designer using the proposed optimization strategy.