Search Results (19)

There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer normal-form games. While counterfactual regret minimization and fictitious play are scalable to large games and have convergence guarantees in two-player zero-sum games, they do not guarantee convergence to Nash equilibrium in multiplayer games. We present an approach for exact computation of Nash equilibrium in multiplayer imperfect-information games that solves a quadratically-constrained program based on a nonlinear complementarity problem formulation from the sequence-form game representation. This approach capitalizes on recent advances for solving nonconvex quadratic programs. Our algorithm is able to quickly solve three-player Kuhn poker after removal of dominated actions. Of the available algorithms in the Gambit software suite, only the logit quantal response approach is successfully able to solve the game; however, the approach takes longer than our algorithm and also involves a degree of approximation. Our formulation also leads to a new approach for computing Nash equilibrium in multiplayer normal-form games which we demonstrate to outperform a previous quadratically-constrained program formulation. Full article

With the advancement of the dual carbon goals and the rapid increase in the proportion of new energy installations, the power system faces multiple challenges including insufficient flexibility resources, intensified fluctuations in generation and load, and reduced operational safety. Integrated energy systems (IESs), serving as key platforms for integrating diverse energy sources and flexible resources, possess complex internal structures and limited individual regulation capabilities, making direct participation in grid dispatch and market interactions challenging. To achieve large-scale resource coordination and efficient utilization, this paper investigates external characteristic modeling and cluster aggregation optimization methods for IES, proposing a comprehensive technical framework spanning from individual external characteristic identification to cluster-level coordinated control. First, addressing the challenge of unified dispatch for heterogeneous resources within IES, this study proposes an external characteristic modeling method based on operational feasible region projection. It constructs models for the active power output boundary, marginal cost characteristics, and ramping rate of virtual power plants (VPPs), enabling quantitative representation of their overall regulation potential. Second, a cluster aggregation optimization model for integrated energy systems is established, incorporating regional autonomy. This model pursues multiple objectives: cost–benefit matching, maximizing renewable energy absorption rates, and minimizing peak external power purchases. The Gini coefficient and Shapley value method are introduced to ensure fairness and participation willingness among cluster members. Furthermore, an optimization mechanism incorporating key constraints such as cluster scale, grid interaction, and regulation complementarity is designed. The NSGA-II multi-objective genetic algorithm is employed to efficiently solve this high-dimensional nonlinear problem. Finally, simulation validation is conducted on a typical regional energy scenario based on the IEEE-57 node system. Results demonstrate that the proposed method achieves average daily cost savings of approximately 3955 CNY under the optimal aggregation scheme, reduces wind and solar curtailment rates to 5.38%, controls peak external power purchases within 2292 kW, and effectively incentivizes all entities to participate in coordinated regulation through a rational benefit distribution mechanism. Full article

In this paper, we propose a penalty approach for solving generalized absolute value equations (GAVEs) of the type $Ax-B\left|x\right|=b$, $(A,B\in {\mathbb{R}}^{n\times n},b\in {\mathbb{R}}^n)$. Firstly, we reformulate the GAVEs as variational inequality problems passing through an equivalent horizontal linear complementarity problem. To approximate the resulting variational inequality, a sequence of nonlinear equations containing a penalty term is then defined. Under a mild assumption, we show that the solution of the considered sequence converges to that of GAVE if the penalty parameter tends to infinity. An algorithm is developed where its corresponding theoretical arguments are well established. Finally, some numerical experiments are presented to show that our approach is quite appreciable. Full article

Aiming at the problem that it is difficult to effectively characterize the operation status of hydropower units with a single vibration signal feature under the influence of multiple factors such as water–machine–electricity coupling, a multidimensional fusion feature extraction method for hydroelectric units based on time–frequency analysis and unsupervised learning models is proposed. Firstly, the typical time–domain and frequency–domain characteristics of vibration signals are calculated through amplitude domain analysis and Fourier transform. Secondly, the time–frequency characteristics of vibration signals are obtained by combining the complementary ensemble empirical mode decomposition and energy moment calculation methods to supplement the traditional time–domain and frequency–domain characteristics, which have difficulty in comprehensively reflecting the correlation between nonlinear non–stationary signals and the state of the unit. Finally, in order to overcome the limitations of shallow feature extraction relying on artificial experience, a Stacked Denoising Autoencoder is used to adaptively mine the deep features of vibration signals, and the extracted features are fused to construct a multidimensional feature vector of vibration signals. The proposed multidimensional information fusion feature extraction method is verified to realize the multidimensional complementarity of feature attributes, which helps to accurately distinguish equipment state types and provides the foundation for subsequent state identification and trend prediction. Full article

This paper is concerned with the modeling of power dissipation due to friction and its relation with wear estimation in wheel–rail contact. Wear is a complex multi-scale and multi-physical phenomenon appearing in rolling contact. Wear is generated by high contact stress and the work of friction forces. This phenomenon leads to the appearing of the worn material in the form of wear debris between contacting surfaces. In contact models, wear is usually described in terms of the wear depth function. This function modifies the gap between the contacting bodies as well as the shape of the surfaces of the wheel and rail in contact. In this paper, besides the wear depth function, the dissipated energy, rather than the contact stress, is taken into account to evaluate the wear impact on rail or wheel surfaces. The dissipated energy allows us to more precisely evaluate the wear debris amount as well as the depth of wear and its distribution along the contact interface. A two-dimensional rolling contact problem with frictional heat flow is considered. The elasto-plastic deformation of the rail is considered. This contact problem is governed by a coupled system of mechanical and thermal equations in terms of generalized stresses, displacement and temperature. The finite element method is used to discretize this problem. A discretized system of equations with nonpenetration and friction conditions is transformed and formulated as a nonlinear complementarity problem. The generalized Newton method is applied to numerically solve this mechanical subproblem. The Cholesky method is used to find the solution of the heat-conductive problem. The dissipated power is evaluated based on the resultant force and slip at a reference point. Numerical results including the distribution of slip velocity, power factor and wear rate are provided and discussed. Full article

We discuss the weighted complementarity problem, extending the nonlinear complementarity problem on $R^n$. In contrast to the NCP, many equilibrium problems in science, engineering, and economics can be transformed into WCPs for more efficient methods. Smoothing Newton algorithms, known for their at least locally superlinear convergence properties, have been widely applied to solve WCPs. We suggest a two-step Newton approach with a local biquadratic order convergence rate to solve the WCP. The new method needs to calculate two Newton equations at each iteration. We also insert a new term, which is of crucial importance for the local biquadratic convergence properties when solving the Newton equation. We demonstrate that the solution to the WCP is the accumulation point of the iterative sequence produced by the approach. We further demonstrate that the algorithm possesses local biquadratic convergence properties. Numerical results indicate the method to be practical and efficient. Full article

We adopt the alternating direction search pattern method to solve the equality and inequality constrained nonlinear optimization problems. Firstly, a new augmented Lagrangian function with a nonlinear complementarity function is proposed to transform the original constrained problem into a new unconstrained problem. Under appropriate conditions, it has been proven that there is a 1-1 correspondence between the local and global optimal solutions of the new unconstrained problem and the original constrained problem. In this way, the optimal solution of the original problem can be obtained by solving the new unconstrained optimization problem. Furthermore, based on the characteristics of the new problem, the alternating direction pattern search method was designed and its convergence was demonstrated. Numerical experiments were implemented to illustrate the availability of the new augmented Lagrangian function and the algorithm. Full article

In order to solve issues that arise in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization issues, equilibrium problems, complementarity issues, selection and matching problems, and issues proving the existence of solutions to integral and differential equations, fixed point theory provides vital tools. In this study, we discuss topological structure and several fixed-point theorems in the context of generalized neutrosophic cone metric spaces. In these spaces, the symmetric properties play an important role. We examine the existence and a uniqueness of a solution by utilizing new types of contraction mappings under some circumstances. We provide an example in which we show the existence and a uniqueness of a solution by utilizing our main result. These results are more generalized in the existing literature. Full article

Linear complementarity problem (LCP) is studied. After reforming general LCP as the system of nonlinear equations by NCP-function, LCP is equivalent to solving an unconstrained optimization model, which can be solved by a recently proposed algorithm named novel global harmony search (NGHS). NGHS algorithm can overcome the disadvantage of interior-point methods. Numerical results show that the NGHS algorithm has a higher rate of convergence than the other HS variants. For LCP with a unique solution, NGHS converges to its unique solution. For LCP with multiple solutions, NGHS can find as many solutions as possible. Meanwhile, for unsolvable LCP, all algorithms are terminated on the solution with the minimum error. Full article

Over the conventional limit equilibrium method and limit analysis method, the finite element method is advantageous, especially for slopes involving complex failure mechanisms where the critical slip surfaces cannot be represented by log spirals and other similarities. In the presence of tension cracks at slope crests, however, the finite element method encounters difficulties in convergence while handling Mohr–Coulomb’s yielding surfaces with tensile strength cut-off. Meanwhile, the commonly used load-controlled method for the system of nonlinear equilibrium equations is hard to bring the slope into the limit equilibrium state. The two drawbacks drag down the finite element method in more extensive applications. By reducing the constitutive integration of plasticity with non-smooth yielding surfaces to the mixed complementarity problem, the convergence in numerical constitutive integration is established for arbitrarily large incremental strains. In order to bring the slope to the limit equilibrium state, a new displacement-controlled algorithm is designed for the system of nonlinear equilibrium equations, which is far more efficient than the load-controlled method. A procedure is proposed to locate tension cracks. Corresponding to the Mohr–Coulomb failure criterion with and without tensile strength cut-off, the failure mechanisms differ significantly, while the difference in the factor of safety might be ignorable. Full article

In this paper, the problem of reliable control design with mixed $H_{\infty }$ /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed $H_{\infty }$ /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature. Full article

This paper provides an empirical analysis of the relationship between debt and national output mediated by a measure of the quality of state governance. Using WGIs dataset of 106 countries for the period 1996–2015, the paper analyzes the mediated effect of governance on debt-growth relationship. For this purpose, we use the fixed effect (LSDV) and system GMM estimation technique in order to overcome the possible problem of endogeneity. Results show the non-linear pattern between public debt and economic growth via governance. Although, public debt has negative impact on economic growth, but the results are statistically positive and significant when public debt is interacted with governance, which confirms that governance is a channel by which public debt influences economic growth. Moreover, we calculate the threshold of governance which shows that the public debt has positive impact on economic growth when the governance level is higher than the threshold and adversely affects the economic growth in the case of low level of governance than threshold. Evidence from this study reveals the fact that governance plays a mediating role in debt-growth relationship as there is a pattern of complementarity between public debt and governance: the higher the level of governance, the lesser the adverse effect of public debt on economic growth. Full article

Water loss according to water leakages in water distribution systems (WDSs) is a challenging problem worldwide. An inappropriate operation of the WDS leads to unnecessarily high pressure distribution in the WDS and thus a large amount of water leakage exists. For this reason, optimal pressure management in WDSs through regulating operations of pressure reducing valves (PRVs) is priority for water utilities. The pressure management can be accomplished in a hierarchical control scheme with high level and low level controllers. While the high level controller is responsible for calculating pressure set points for critical nodes, the task of a low level controller is to regulate the pressures at the critical nodes to the set points. The optimal pressure management in the high level controller can be casted into a nonlinear programing problem (NLP) where PRV models are crucial and determine proper operation of the WDS and quality of overall pressure control. PRV models having been used until now either describe two operating modes (active and open modes) or three operating modes (active, open and check valve modes) with parameter dependence. Such models make the formulated NLP unsuitable for the case PRVs work in check valve modes or resulted in inaccurate NLP solution with unexpected operation modes of PRVs, respectively. Therefore, this paper proposes an accurate PRV model based on complementarity constraints. The new PRV model is parameter-less dependence and is capable of describing complete operation modes of PRVs in practice. As a result, the formulated NLP is general and provides accurate NLP solution. The efficiency of our new PRV model is demonstrated on numerous case studies for optimal pressure management of WDSs. Full article

The question of whether the liberalization of the gas industry has led to less concentrated markets has attracted much interest among the scientific community. Classical mathematical regression tools, statistical tests, and optimization equilibrium problems, more precisely non-linear complementarity problems, were used to model European gas markets and their effect on prices. In this research, the parametric and nonparametric game theory methods are employed to study the effect of the market concentration on gas prices. The parametric method takes into account the classical Cournot equilibrium test, with assumptions on cost and demand functions. However, the non-parametric method does not make any prior assumptions, a factor that allows greater freedom in modeling. The results of the parametric method demonstrate that the gas suppliers’ behavior in Austria and The Netherlands gas markets follows the Nash–Cournot equilibrium, where companies act rationally to maximize their payoffs. The non-parametric approach validates the fact that suppliers in both markets follow the same behavior even though one market is more liquid than the other. Interestingly, our findings also suggest that some of the gas suppliers maximize their ‘utility function’ not by only relying on profit, but also on some type of non-profit objective, and possibly collusive behavior. Full article

In this paper, we propose a new version of the generalized damped Gauss–Newton method for solving nonlinear complementarity problems based on the transformation to the nonsmooth equation, which is equivalent to some unconstrained optimization problem. The B-differential plays the role of the derivative. We present two types of algorithms (usual and inexact), which have superlinear and global convergence for semismooth cases. These results can be applied to efficiently find all solutions of the nonlinear complementarity problems under some mild assumptions. The results of the numerical tests are attached as a complement of the theoretical considerations. Full article