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This paper is intended as a companion to [12] and focuses on the numerical implementations of the method in the context of insurance problems with mixed controls: reinsurance acting as continuous control, and capital injection and dividend payment acting as singular ones. The aim is twofold. On the one hand, we provide a comparison of the output of our method in terms of the optimal value against two benchmarks. The first benchmark is provided by [4] in the no-reinsurance setting and when the claims are exponentially distributed. The second benchmark refers to [8] where capital injections are not permitted, but different claim distributions can be employed. On the other hand, we illustrate the improvement of the models in [8] when capital injection is allowed. We also look into the effect of reinsurance in the model [4]. Several cases for the equity cost parameter are discussed as are the boundary (or limit) situations. • We provide a validation of the Dual Linear Programming algorithm by showcasing its performance on two benchmarks. • With a relatively modest order of moments (4), the relative errors are of at most 3%. • Leveraging this algorithm reveals significant enhancements in the expected dividends, advocating for capital injections. [ABSTRACT FROM AUTHOR]

In the theory and applications of graphs, it is a basic problem to compute the numbers of independent sets and matchings of given sizes. Since the problem of computing the total number of independent sets and that of matchings of graphs is #P-complete, it is unlikely to give efficient algorithms to find the numbers of independent sets and matchings of given sizes. In this paper, for graphs with order n and treewidth at most p , we present two dynamic algorithms to compute the numbers of independent sets of all sizes with runtime O (2 p  ·  pn 3 ) and the numbers of matchings of all sizes with runtime O (2 2 p  ·  pn 3 ), respectively. By the algorithms presented in this paper, for graphs with small treewidths, the numbers of independent sets and matchings of all possible sizes can be computed efficiently. [ABSTRACT FROM AUTHOR]

This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cramér-Lundberg claims, by allowing singular dividend payments and capital injections. Using variational techniques and embedding the trajectories in an appropriate family of occupation measures, we provide the linearisation of such problems in which the continuous control is given by reinsurance policies and the singular one by dividends and capital injections. The linearisation translates into a dual dynamic programming (DDP) algorithm. An important part of the paper is dedicated to structural considerations allowing reasonable implementation. We also hint connections to methods relying on moment sum of squares and LMI (linear matrix inequality)-relaxations to approximate the optimal candidates. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a nonlinear Lagrangian Based on Fischer-Burmeister NCP function for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. Moreover, the paper develops the dual approach associated with the proposed nonlinear Lagrangian, in which the related duality theorem is demonstrated. Furthermore, it is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Numerical results for solving several nonlinear programming problems are reported, showing that the new nonlinear Lagrangian is superior over other known nonlinear Lagrangians for solving some nonlinear programming problems. [Copyright &y& Elsevier]

Abstract: In this paper, we present a comprehensive empirical analysis of the Vertex Contraction (VC) algorithm for the problem of checking whether a directed graph with positive and negative costs on its edges has a negative cost cycle (NCCD). VC was first presented in [K. Subramani, L. Kovalchick, Contraction versus relaxation: a comparison of two approaches for the negative cost cycle detection problem, in: P.M.A. Sloot et al. (Ed.), Proceedings of the third international conference on computational science (ICCS), Lecture notes in computer science, vol. 2659, Springer-Verlag, 2003, pp. 377–387] and is the only known purely greedy strategy for the NCCD problem. In [K. Subramani, L. Kovalchick, Contraction versus relaxation: a comparison of two approaches for the negative cost cycle detection problem, in: P.M.A. Sloot et al. (Ed.), Proceedings of the third international conference on computational science (ICCS), Lecture notes in computer science, vol. 2659, Springer-Verlag, 2003, pp. 377–387], we compared the performance profiles of a naive implementation of VC and the “standard” Bellman–Ford (BF) algorithm for negative cost cycle detection; we observed that VC performed an order of magnitude better than the BF algorithm. Our experiments were conducted on a range of randomly generated inputs over multiple classes of networks and the results conclusively demonstrated the superiority of VC over a naive implementation of BF. Our observations are surprising given that VC is asymptotically inferior to BF on sparse networks. This paper continues the study of contrasting greedy and dynamic programming (relaxation-based) approaches for the NCCD problem, by comparing sophisticated variants of VC with sophisticated implementations of the BF algorithm. Variants of VC are obtained by employing different heuristics to determine the vertex contraction sequence, in precisely the same manner as variants of BF are obtained by employing different heuristics to determine the edge relaxation sequence. Our experiments indicate that on most classes of networks, there is at least one VC variant with a performance profile that is comparable to the more sophisticated BF implementations. Our results are most surprising for the case of planar networks, where a variant of VC performs almost as well as the best relaxation-based algorithm. One of the principal conclusions of our work is that a simple, greedy approach involving vertex contraction is a good choice on sparse networks. On a more fundamental note, we establish that the selection of an algorithm for the NCCD problem should involve an analysis of the input and the architecture of the computing machine, in order to maximize performance. [Copyright &y& Elsevier]

• A new kind of data-based fault detection method is proposed, which combines adaptive dynamic programming and multiple-modeling. • A stable working state is established by using ADP and history data. Once the system runs out of the stable state, it's known for sure that fault occurs. • A whole stable working space of the system can be built with the method of multi-modeling and data of all working modes, as long as system states remain in the working space, system is working normally, exclude the disturbance of modes switching, and improve the accuracy of the fault detection algorithm. • The fault can be isolated, if the direction and magnitude of the deviate vector are solved, which can be achieved by approximation and iteration using the method of ADP. This paper presents a adaptive dynamic programming-based fault detection and isolation (FDI) scheme to detect and isolate faults in an aircraft jet engine. To this end, the weights in Actor-Critic neural networks are first tuned to learn the input-output map of the jet engine considering its multiple working modes. The convergences of the trainings in Critic-Actor neural networks are strictly proved without knowing the drift dynamics and the input dynamics in the presence of unknown nonlinearities and approximation errors. Using the residuals that are generated by measuring the difference of each network output and the measured engine output, various criteria are established for accomplishing the fault diagnosis task, that addresses the problem of fault detection and isolation of the system components. A number of simulation studies are carried out for combustion chamber of a single-spool jet engine to demonstrate and illustrate the advantages, capabilities, and performance of our proposed fault diagnosis scheme. [ABSTRACT FROM AUTHOR]

• This article develops an online ADP method for discrete nonlinear systems, it can reduce the computation burden. • Two ESNs are employed to implement the online learning and the output weights are obtained simultaneously. • The hidden layer of ESN is generated randomly rather than designed with much effort, which reduces the application complexity. This paper investigates the online optimal control problem of discrete-time nonlinear systems using echo state network (ESN)-based adaptive dynamic programming (ADP) method. An online iterative learning algorithm is proposed to solve the partial differential Hamilton–Jacobi–Bellman (HJB) equation in real time. A novel neural networks (NN) critic-actor architecture is presented using two ESNs to implement the ADP method. Then, two online learning laws of the output weights are designed for searching the optimal cost function and control policy. The stability of system and output weights is analysed using Lyapunov approach. Three simulations are given to show the feasibility and effectiveness of the designed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: The discounted {0–1} knapsack problem (DKP) is an extension of the classical {0–1} knapsack problem (KP) that consists of selecting a set of item groups where each group includes three items and at most one of the three items can be selected. The DKP is more challenging than the KP because four choices of items in an item group diversify the selection of the items. Consequently, it is not possible to solve the DKP based on a classical definition of a core consisting of a small number of relevant variables. This paper partitions the DKP into several easier sub-problems to achieve problem reductions by imitating the core concept of the KP to derive an alternative core for the DKP. Numerical experiments with DP-based algorithms are conducted to evaluate the effectiveness of the problem partition by solving the partitioned problem and the original problem based on different types of DKP instances. [Copyright &y& Elsevier]

Abstract: Minesweeper is a popular single player game. It has been shown that the Minesweeper consistency problem is NP-complete and the Minesweeper counting problem is #P-complete. In this paper, we present efficient algorithms for solving these problems for Minesweeper graphs with bounded treewidth. Our algorithms turn out to be much better than those based directly on dynamic programming. The algorithms mostly use of algebraic operations on multivariate polynomials, so that one may use existing software to implement them easily. [Copyright &y& Elsevier]

Abstract: Recently, an efficient reversible lossless data hiding algorithm by Ni et al. was presented. Their fast algorithm can recover the original image without any distortion and its PSNR lower bound is higher than that of all existing reversible data hiding algorithms. Instead of selecting the peak-valley pairs in a greedy way, this paper presents a dynamic programming-based reversible data hiding algorithm to determine the most suitable peak-valley pairs such that the embedding capacity object can be maximized. Based on some artificial map images, experimental results demonstrate that our proposed algorithm has 9% embedding capacity improvement ratio and has the similar image quality performance when compared to Ni et al.’s algorithm although it has some execution-time degradation. For natural images, the embedding capacity of Ni et al.’s algorithm is very close to the maximal embedding capacity obtained by our proposed algorithm. Furthermore, the comparison between our proposed dynamic programming-based algorithm and the reversible data hiding algorithm by Chang et al. is investigated. [Copyright &y& Elsevier]

Abstract: An active area of research for linear programming is to construct initial Simplex tableau that is close to the optimal solution, and to improve its pivoting selection strategies efficiently. In this paper, we present a new approach to the problem of initialization and pivoting rules: the algorithm is free from any artificial variables and artificial constraints, known as the big-M methods. By supplying the Simplex method without using any large numbers, therefore the result is computationally stable and provides a better initial basis that reduces the number of pivoting iterations efficiency. A three-phase simplex type solution algorithm is developed for solving general linear programs. In phase 1, greater-than constraints are relaxed and the problem is solved starting at the origin. If it is unbounded; then the objective function is modified in order to have a bound feasible solution. Then, in phase 2 the greater-than constraints are introduced in a dual simplex framework. Following this, in the case the original objective function was modified, phase 3 restores optimality for the original objective function. The algorithm is numerically stable and works with the original decision variables. Our initial experimental study indicates that the proposed algorithm is more efficient than both the primal and the dual simplex in terms of the number of iterations. [Copyright &y& Elsevier]

Abstract: A multiple-choice knapsack problem can be formulated as a discrete nonlinear knapsack problem (DNKP). A powerful method for solving DNKP is the dynamic programming solution approach. The use of this powerful approach however is limited since the growth of the number of decision variables and state variables requires an extensive computer memory storage and computational time. In this paper we developed a hybrid algorithm for improving the computational efficiency of the dynamic programming when it is applied for solving the DNKP. In the hybrid algorithm, three routines of the imbedded state, surrogate constraints, and bounding scheme are incorporated for increasing the efficiency of this solution approach. We then conducted an experimental study for comparing the computational efficiency of the hybrid algorithm with the imbedded state dynamic programming approach. [Copyright &y& Elsevier]

Abstract: Recently, filter methods are extensively studied to handle nonlinear programming problems. Because of good numerical results, filter techniques are attached importance to. In this paper, filter approaches are employed to tackle nonlinear complementarity problems. Furthermore, a new filter algorithm is brought forward. Under a proper condition, local Q-superlinear and Q-quadratic convergence of the algorithm is established. [Copyright &y& Elsevier]

Abstract: This paper presents a global optimization algorithm for a class of multiplicative programming with exponent under multiplicative constraints (MPE). By utilizing equivalent problem of MPE in the sense that they have the same optimal solution, tangential hypersurfaces and concave envelope approximations a linear relaxation of equivalent problem is received. Thus the initial nonconvex programming problem (MPE) is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region of the objective function. The proposed algorithm is convergent to the globally optimal solution of MPE by means of the subsequent solutions of a series of linear programming problems. Numerical results indicate that the proposed algorithm is extremely robust and can be used successfully to solve global minimum of MPE on microcomputer. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the analysis of a discrete-time dynamic programming algorithm for the numerical solution of an optimal asset–liability management model with transaction costs and in presence of constraints. By exploiting the financial properties of the model, we propose an approximation method based on the classical dynamic programming algorithm, which reduces significantly the computational and storage requirements of the algorithm and avoids any artificial boundary condition. The regularity of the value function is used to estimate the global error introduced by the numerical procedure and to prove a convergence result. [Copyright &y& Elsevier]

In this paper, we characterize the optimal profit (best return) of an investment problem with trapezoidal fuzzy numbers. We give a solution algorithm to determine the optimal profit for investing of F money in the n investment polices. Alternative approach is considered for people who need to be more precise in their requirements. Illustrative example to determine the optimal profits of such problem, is presented. [Copyright &y& Elsevier]