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AbstractAccurate estimation of frictional pressure loss in an annulus is crucial for selecting appropriate pump systems, determining horsepower requirements, and controlling hole cleaning. Generally, when calculating the friction factor, the temperature of the fluid and the rotation of the inner pipe are not considered, which can lead to errors in estimating the pressure difference in the annulus. In this study, to ensure accurate pressure drop calculations, the effects of temperature and inner pipe rotation, along with other parameters, were included. An extensive experimental study was conducted at Izmir Katip Celebi University’s Flow Loop using two Carboxymethyl cellulose (CMC) solutions, across various fluid velocities, fluid temperatures, diameter ratios, and inner pipe rotation speeds. A dimensional analysis was performed to identify the parameters that affect friction factors in the annulus. Finally, friction factor equations were developed based on the experimental data using optimization algorithms such as interior point (fmincon), genetic, minimax, and simulated annealing. The findings showed that the predictions from all the algorithms tested in the study closely matched the experimental results; however, the interior point algorithm (fmincon) provided the best performance, with an average absolute percentage error of 9.4%. [ABSTRACT FROM AUTHOR]

This research implements an evolutionary optimized finite differences scheme (FDS) for nonlinear electrohydrodynamics ion drag flow dynamics in a cylindrical conduit (EHD-IDFCC). In the scheme, finite differences are exploited to discretize governing expressions of EHD-IDFCC, represented with a nonlinear singular seconder order differential equation, into a nonlinear equations-based system. The fitness function based on residual error is constructed for the FDS-based discretized EHD-IDFCC model. Its optimization is conducted with the global search capability of genetic algorithms (GAs) aided by the local search efficacy of the interior-point method (IPM), i.e., FDS-GA-IPM. The performance of the designed stochastic numerical solver FDS-GA-IPM is evaluated for a variant of the EHD-IDFCC model for different scenarios to measure the effect of axial flow velocity by varying the electric Hartmann numbers, as well as the nonlinearity factor. Statistical interpretations based on histogram illustrations, probability plots, and boxplots in terms of the cost function, mean absolute error (MAE), Thai inequality coefficients (TIC), and coefficient of determination metrics (R2) are used to endorse the accuracy, convergence, stability, and strength of the FDS-GA-IPM.

This article introduces a novel optimization approach known as fractional order whale optimization algorithm (FWOA). The proposed optimizer incorporates the idea of fractional calculus (FC) into the mathematical structure of the conventional whale optimization algorithm (WOA). To validate the efficiency of the proposed FWOA, it is applied to address the challenges associated with the economic load dispatch (ELD) problem, which is a nonconvex, nonlinear, and non-smooth optimization problem. The objectives associated with ELD such as fuel cost and wind power generation cost minimization are achieved by taking into consideration different practical constraints like valve point loading effect (VPLE), transmission line losses, generator constraints, and stochastically variation of renewable energy sources (RES) integration. RES, particularly wind energy, has garnered more attention in recent times due to a range of environmental and economic factors. Stochastic wind (SW) power is also included in the ELD problem formulation. The incomplete gamma function (IGF) quantifies the influence of wind power. To assess its efficacy, the suggested approach is applied to a range of power systems including 3 generating units, 13 generating units and 40 generating units, consisting of 37 thermal units and 3 wind power units. To further strengthen the performance of the optimizer, the FWOA is hybridized with the interior point algorithm (IPA) to further refine the outcomes of the FWOA. The FWOA and IPA are used to address the problem of ELD while including the unpredictable nature of wind power. The simulation results of the suggested technique are compared with the most advanced heuristic optimization methods available, and it has been observed that the proposed optimizer obtained a superior and refined solution when compared to other state of the art optimization techniques. Furthermore, the efficacy of the suggested strategy in enhancing the solution of the ELD issue is validated through statistical analysis in terms of minimum fitness value. [ABSTRACT FROM AUTHOR]

This research presents a novel methodology for tackling the combined thermal-wind economic load dispatch (ELD) issue in contemporary power system. The proposed approach involves hybridizing active-set algorithm (ASA), interior point algorithm (IPA) and sequential quadratic programming (SQP) into grey wolf optimization (GWO) algorithm, while effectively incorporating the intricacies associated with renewable energy sources (RES). A more accurate model is made possible by hybridization for complex systems with memory and hereditary characteristics. The GWO is used as a tool for global search while ASA, IPA and SQP methods are used for rapid local optimization mechanism. The performance evaluation of the design heuristics is carried out on 37 thermal and 3 wind power generating units and outcomes endorse the effectiveness of the proposed scheme over state-of-the-art counterparts. The worthy performance is further validated on statistical assessments in case of thermal-wind integrated ELD problem in terms of measure of central tendency and variation on cost and complexity indices. [ABSTRACT FROM AUTHOR]

This research presents a novel methodology for tackling the combined thermal-wind economic load dispatch (ELD) issue in contemporary power system. The proposed approach involves hybridizing active-set algorithm (ASA), interior point algorithm (IPA) and sequential quadratic programming (SQP) into grey wolf optimization (GWO) algorithm, while effectively incorporating the intricacies associated with renewable energy sources (RES). A more accurate model is made possible by hybridization for complex systems with memory and hereditary characteristics. The GWO is used as a tool for global search while ASA, IPA and SQP methods are used for rapid local optimization mechanism. The performance evaluation of the design heuristics is carried out on 37 thermal and 3 wind power generating units and outcomes endorse the effectiveness of the proposed scheme over state-of-the-art counterparts. The worthy performance is further validated on statistical assessments in case of thermal-wind integrated ELD problem in terms of measure of central tendency and variation on cost and complexity indices.

This paper presents a Mehrotra-type predictor–corrector algorithm for monotone nonlinear complementarity problems over symmetric cones. The proposed algorithm is a second-order predictor–corrector interior point algorithm. Based on a one-norm wide neighbourhood, the iteration complexity of the algorithm is estimated and some numerical results are provided. The numerical results show that the algorithm is efficient and reliable. [ABSTRACT FROM AUTHOR]

This article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the iteration numbers required for convergence, making it a valuable tool for solving complex optimization problems from FELA. The algorithm also introduces several new features to the existing methods, including: (i) a novel method for determining a reasonable updating step length; (ii) the avoidance of solving an additional "phase one problem" for finding an initial feasible point; and (iii) the proposition of an empirical criterion for detecting infeasibility problems. The effectiveness of the proposed approach has been demonstrated through several classic examples derived from geotechnical engineering. The initial two examples show the superior convergence speed of the novel approach compared to existing methods. Additionally, the third example highlights the efficacy of the feasibility detection criterion for problems involving both prescribed and unknown external forces. [ABSTRACT FROM AUTHOR]

This article introduces a novel optimization approach known as fractional order whale optimization algorithm (FWOA). The proposed optimizer incorporates the idea of fractional calculus (FC) into the mathematical structure of the conventional whale optimization algorithm (WOA). To validate the efficiency of the proposed FWOA, it is applied to address the challenges associated with the economic load dispatch (ELD) problem, which is a nonconvex, nonlinear, and non-smooth optimization problem. The objectives associated with ELD such as fuel cost and wind power generation cost minimization are achieved by taking into consideration different practical constraints like valve point loading effect (VPLE), transmission line losses, generator constraints, and stochastically variation of renewable energy sources (RES) integration. RES, particularly wind energy, has garnered more attention in recent times due to a range of environmental and economic factors. Stochastic wind (SW) power is also included in the ELD problem formulation. The incomplete gamma function (IGF) quantifies the influence of wind power. To assess its efficacy, the suggested approach is applied to a range of power systems including 3 generating units, 13 generating units and 40 generating units, consisting of 37 thermal units and 3 wind power units. To further strengthen the performance of the optimizer, the FWOA is hybridized with the interior point algorithm (IPA) to further refine the outcomes of the FWOA. The FWOA and IPA are used to address the problem of ELD while including the unpredictable nature of wind power. The simulation results of the suggested technique are compared with the most advanced heuristic optimization methods available, and it has been observed that the proposed optimizer obtained a superior and refined solution when compared to other state of the art optimization techniques. Furthermore, the efficacy of the suggested strategy in enhancing the solution of the ELD issue is validated through statistical analysis in terms of minimum fitness value.

In this paper, the parameters of the geared PMDC motor are estimated using the interior point algorithm (IPA). The problem of parameter estimation is converted to an optimization problem. The proposed estimation method measures the current and speed responses of the motor under a step input voltage. The objective of the IPA is to search for the parameters of the simulated PMDC motor in order to minimize the errors between the measured current and speed responses of the PMDC motor and the corresponding responses from the simulated model of the PMDC motor. Steady-state mathematical relations between the geared PMDC motor parameters are derived and used as equality and inequality constraints for constructing the proposed IPA. The proposed IPA is a gradient-based optimization algorithm. Therefore, it can efficiently and quickly minimize the objective function and obtain the solution. Moreover, the proposed estimation algorithm considers the estimation of the Coulomb friction torque of the motor. Hence, seven parameters of the geared PMDC motor are estimated: armature resistance, armature inductance, back EMF constant, torque constant, moment of inertia, viscous friction, and Coulomb friction torque. MATLAB and Arduino IDE software are utilized with the Pololu 25D motor for programming and simulation. The experimental setup is used to obtain the measured current and speed step responses. MATLAB and Simulink are used for modeling the simulated PMDC motor and the implementation of the IPA. Simulation and experimental results express the effectiveness of the proposed estimation algorithm in estimating the geared PMDC motor parameters.

Numerical simulation of fluids is crucial in modeling physical phenomena in various fields, including engineering, physics, and environmental science. Fluids are typically described by the Navier-Stokes equations, but solving these coupled equations for complex models with computational fluid dynamics (CFD) tools remains challenging due to the high computational cost and time required to address the minute interpolation errors. In this article, we have introduced a novel physics-informed machine learning technique that does not rely on any reference dataset to study bioconvection nanofluid flow across an inclined stretching surface. More specifically, a structured physics-informed neural network (PINN) architecture is devised to enforce the initial and boundary conditions. The governing partial differential equations are transformed into third-order nonlinear ordinary differential equations (ODEs). The transformed ODEs are incorporated into the loss of the PINN to drive the training. The weights of PINN are trained with the interior point algorithm (IPA). The effects of the thermophoresis parameter and the Brownian motion parameter on the velocity, temperature, nanoparticle concentration, and microorganisms' density profiles have been graphically presented and analysed by creating two different PINNs in an unsupervised way. The proposed results are compared with traditional finite element solutions, and they show satisfactory agreement with a precision of 2–4 decimal places. Statistical analysis for a large number of independent executions validates the convergence and worth of the proposed approach. The research offers continuous solutions over the whole trained interval with comparable accuracy and paves the way for the application of physics-informed machine learning to complex fluid mechanics and heat transfer problems. [ABSTRACT FROM AUTHOR]

Incorporating numerically predicted responses of seepage characteristics based on large numbers of surrogate models to identify the optimum design of Concrete Gravity Dams (CGD) can lead to sub-optimal or local solution, even when the evolutionary Genetic Algorithm (GA) optimization solver is utilized. The optimization task aims to find the safe and minimum cost design for the CGD built on anisotropic permeable soils, considering the effect of seepage under the CGD. In each iteration of the optimization model solution, the GA-based linked Simulation-Optimization (S-O) approach evaluates the objective function and the constraints based on the responses of the Support Vector Machine (SVM) surrogate models. This paper focused on improving the GA performance to find the global or a near global optimum design of a complex optimization model, minimizing the construction cost, and providing a design safety of the CGD. This could be achieved by using the Hybrid Genetic Algorithm (HGA) optimization solver. The HGA merges two optimization search techniques: the direct search methods utilizing GA, and the gradient search method using the Interior Point Algorithm (IPA). The solution results showed that the HGA was more efficient in finding improved or, global optimum design of the CGD. Physically, the low anisotropic ratio of hydraulic conductivity (0.1, 0.3, 0.5) resulted in critical seepage characteristics, which substantially affects the optimum hydraulic design of CGD, and increases the corresponding construction cost. [ABSTRACT FROM AUTHOR]

Quantile regression is a powerful statistical technique for estimating the quantiles of a conditional distribution on the values of covariates. It has been widely used in many fields. In this paper, an improved interior point algorithm for quantile regression is proposed. The algorithm introduces multiple centrality corrections technique into the interior point algorithm for quantile regression. The purpose of introducing the multiple centrality corrections technique is to reduce the overall solution time required to solve a quantile regression problem. The computational experiments results constitute evidence of the improvement obtained with the use of multiple centrality correction technique combined with the interior point algorithm.

We present a neural network model for estimation of multiple conditional quantiles that satisfies the noncrossing property. Motivated by linear noncrossing quantile regression, we propose a noncrossing quantile neural network model with inequality constraints. In particular, to use the first-order optimization method, we develop a new algorithm for fitting the proposed model. This algorithm gives a nearly optimal solution without the projected gradient step that requires polynomial computation time. We compare the performance of our proposed model with that of existing neural network models on simulated and real precipitation data. for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper we propose a robust and efficient primal-dual interior-point method for a nonlinear ill-conditioned problem with associated errors which are arising in the unfolding procedure for neutron energy spectrum from multiple activation foils. Based on the maximum entropy principle and Boltzmann's entropy formula, the discrete form of the unfolding problem is equivalent to computing the analytic center of the polyhedral set P = { x ∈ Rn ∣ Ax = b,x ≥ 0}, where the matrix A ∈ Rm×n is ill-conditioned, and both A and b are inaccurate. By some derivations, we find a new regularization method to reformulate the problem into a well-conditioned problem which can also reduce the impact of errors in A and b. Then based on the primal-dual interior-point methods for linear programming, we propose a hybrid algorithm for this ill-conditioned problem with errors. Numerical results on a set of ill-conditioned problems for academic purposes and two practical data sets for unfolding the neutron energy spectrum are presented to demonstrate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a variant of Mehrotra-type predictor–corrector algorithm is proposed for P∗(κ) $P_{*}(\kappa )$ linear complementarity problems. In this algorithm, a safeguard step is used to avoid small step sizes and a new corrector direction is adopted. The algorithm has polynomial iteration complexity and the iteration bound is O((14κ+11)(1+4κ)(1+2κ)nlog(x0)Ts0ε) $O ((14\kappa +11)\sqrt{(1+4 \kappa )(1+2\kappa )}~n\log \frac{(x^{0})^{T}s^{0}}{\varepsilon } )$. Some numerical results are reported as well.

In this paper, a novel meta-heuristic computing solver is presented for solving the singular three-point second-order boundary value problems using artificial neural networks (ANNs) optimized by the combined strength of global and local search ability of genetic algorithms (GAs) and interior point algorithm (IPA), i.e., ANN–GA–IPA. The inspiration for presenting this numerical work comes from the intention of introducing a consistent framework that combines the effective features of neural networks optimized with the contexts of soft computing to handle with such challenging systems. Three numerical variants of singular second-order system have been taken to examine the proficiency, robustness, and stability of the designed approach. The comparison of the proposed results of ANN–GA–IPA from available exact solutions shows the good agreement with 5 to 7 decimal places of the accuracy which established worth of the methodology through performance analyses on a single and multiple executions. [ABSTRACT FROM AUTHOR]

Supervised stereo matching costs need to learn model parameters from public datasets with ground truth disparity maps. However, it is not so easy to obtain the ground truth disparity maps, thus making the supervised stereo matching costs difficult to apply in practice. This paper proposes an unsupervised stereo matching cost based on sparse representation (USMCSR). This method does not rely on the ground truth disparity maps, besides, it also can reduce the effects of the illumination and exposure changes, thus making it suitable for measuring similarity between pixels in stereo matching. In order to achieve higher computational efficiency, we further propose an efficient parallel method for solving sparse representation coefficients. The extended experimental results on three commonly used datasets demonstrate the effectiveness of the proposed method. Finally, the verification results on the monocular video clip show the USMCSR can also work well without ground truth disparity maps. [ABSTRACT FROM AUTHOR]

One of the fundamental challenges of deploying sensor networks in applications, such as environmental monitoring and surveillance, is power management in the presence of various constraints. To address this challenge, in this paper, three problems over asymmetric networks represented by weighted directed graphs (digraphs) are investigated using a distributed approach. The first problem relates to transmission power control over the network to maximize connectivity. It is assumed that different nodes use different transmission power levels to communicate with their neighbors. The notion of generalized algebraic connectivity (GAC), used as a network connectivity measure, is formulated as an implicit function of the network's transmission power matrix. An optimization problem is introduced to maximize the network GAC while satisfying constraints on communication transmission powers. The second problem is the dual of the first one, i.e., minimizing the total transmission power of the network while controlling the network GAC. Ultimately, a third optimization problem is formulated to maximize the lifetime of the network and control its connectivity. Asymptotic convergence of the proposed algorithms to a local or global optima of the original optimization problems are demonstrated analytically. The effectiveness of the proposed distributed algorithm is verified by simulations.

Summary: Power flow control in the power system aims to supply electricity to customers efficiently and low operating costs. Based on the conventional approach, the electric power operators only emphasize the function of optimizing generating costs according to load demand and active power limits of generators. On the other hand, the adjustment of the optimization results requires manual adjustments in its implementation. The optimization of the fuel costs minimization, which involves all constraints, is very expected by the operators so that the operator can implement the results directly without making any adjustments. Furthermore, the constraints in power flow optimization that consist of generator capability curve limits, voltage limits, transmission line limits, and active power limits on generators will lead to more complicated optimization, and the application program will run slowly. This paper proposes a method that can reduce optimization constraints with less computation time. The method is to reduce the limits of the generator capability curve through a mathematical model. While the optimization method used is the predictor‐correctors techniques and reduction techniques in the interior point algorithm. The method uses a simple power system using a four‐bus power system that provides accurate and satisfying results. Besides, this method has been successfully implemented in a large‐scale system, namely, the 500 kV Java—Bali Power System with 65 buses and 40 generating units. [ABSTRACT FROM AUTHOR]

Power curves provided by wind turbine manufacturers are obtained under certain conditions that are different from those of real life operation and, therefore, they actually do not describe the behavior of these machines in wind farms. In those cases where one year of data is available, a logistic function may be fitted and used as an accurate model for such curves, with the advantage that it describes the power curve by means of a very simple mathematical expression. Building such a curve from data can be achieved by different methods, such as using mean values or, alternatively, all the possible values for given intervals. However, when using the mean values, some information is missing and when using all the values the model obtained can be wrong. In this paper, some methods are proposed and applied to real data for comparison purposes. Among them, the one that combines data clustering and simulation is recommended in order to avoid some errors made by the other methods. Besides, a data filtering recommendation and two different assessment procedures for the error provided by the model are proposed. [ABSTRACT FROM AUTHOR]

In this study, a stochastic numerical technique is used to investigate the numerical solution of heat transfer temperature distribution system using feed forward artificial neural networks. Mathematical model of fin equation is formulated with the help of artificial neural networks. The effect of the heat on a rectangular fin with thermal conductivity and temperature de-pendent internal heat generation is calculated through neural networks optimization with optimizers like active set technique, interior point technique, pattern search, genetic algorithm and a hybrid approach of pattern search - interior point technique, genetic algorithm - active set technique, genetic algorithm - interior point technique, and genetic algorithm - sequential quadratic programming with different selections of weights. The governing fin equation is transformed into an equivalent non-linear second order ODE. For this transformed ODE model we have performed several simulations to provide the justification of better convergence of results. Moreover, the effectiveness of the designed models is validated through a complete statistical analysis. This study reveals the importance of rectangular fins during the heat transformation through the system. [ABSTRACT FROM AUTHOR]

We propose an interior point method to compute solution of linear complementarity problem LCP (q, A) given that A is a real square hidden Z-matrix (generalization of Z-matrix) and q is a real vector. The class of hidden Z-matrix is important in the context of mathematical programming and game theory. We study the solution aspects of linear complementarity problem with A ∈ hidden Z-matrix. We observe that our proposed algorithm can process LCP (q, A) in polynomial time under some assumptions. Two numerical examples are illustrated to support our result. [ABSTRACT FROM AUTHOR]

The paper presents the equal tendency algorithm for approximating the reliability problem. The algorithm is based on the fact that a reliability product of various components tends to be maximal if the individual components are approximately equal. The nonlinear integer reliability problem is approximated as a binary linear integer model using the equal tendency theorem. The resulting linear model is then solved using the available efficient interior point algorithms. [ABSTRACT FROM AUTHOR]

This paper establishes a theoretical framework of infeasible Mehrotra-type predictor-corrector algorithm for Cartesian nonlinear complementarity problems over symmetric cones which can be regarded as an extension of Liu et al. [Polynomial convergence of Mehrotra-type predictor-corrector algorithm for the Cartesian -LCP over symmetric cones, Optimization 64(4) (2013), pp. 1-23] for Cartesian linear complementarity problems over symmetric cones to Cartesian nonlinear complementarity problems over symmetric cones. The iteration complexities of the proposed algorithm are estimated and some numerical results are provided. The numerical results show that the proposed algorithm is efficient and reliable. [ABSTRACT FROM AUTHOR]

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Power curves provided by wind turbine manufacturers are obtained under certain conditions that are different from those of real life operation and, therefore, they actually do not describe the behavior of these machines in wind farms. In those cases where one year of data is available, a logistic function may be fitted and used as an accurate model for such curves, with the advantage that it describes the power curve by means of a very simple mathematical expression. Building such a curve from data can be achieved by different methods, such as using mean values or, alternatively, all the possible values for given intervals. However, when using the mean values, some information is missing and when using all the values the model obtained can be wrong. In this paper, some methods are proposed and applied to real data for comparison purposes. Among them, the one that combines data clustering and simulation is recommended in order to avoid some errors made by the other methods. Besides, a data filtering recommendation and two different assessment procedures for the error provided by the model are proposed.

This paper provides an analysis of the iterative complexities of a class of homogeneous algorithms for monotone nonlinear complementarity problems over symmetric cones. The proof of the complexity bounds requires that the nonlinear transformation satisfies an SLC. To prove the complexity bounds of the homogeneous algorithm, this paper proposes an SLC which does not depend on the scaling parameter p and is very easy to be verified. More important, it has scaled invariance. Underlying SLC, the obtained complexity bounds of the short-step algorithm, the semi-long-step algorithm and the long-step algorithm with the sx-direction match that of the homogeneous algorithms proposed by Yoshise [Homogenous algorithms for monotone complementarity problems over symmetric cones. Pac J Optim. 2008; 5(2):313-337]. [ABSTRACT FROM AUTHOR]

We design a grey wolf optimizer hybridized with an interior point algorithm to correct a faulty antenna array. If a single sensor fails, the radiation power pattern of the entire array is disturbed in terms of sidelobe level (SLL) and null depth level (NDL), and nulls are damaged and shifted from their original locations. All these issues can be solved by designing a new fitness function to reduce the error between the preferred and expected radiation power patterns and the null limitations. The hybrid algorithm has been designed to control the array’s faulty radiation power pattern. Antenna arrays composed of 21 sensors are used in an example simulation scenario. The MATLAB simulation results confirm the good performance of the proposed method, compared with the existing methods in terms of SLL and NDL. [ABSTRACT FROM AUTHOR]

In this paper, we establish a theoretical framework of infeasible path-following interior point algorithm for Cartesian nonlinear complementarity problems over symmetric cones using a wide neighbourhood of the central path. In order to prove the convergence of the proposed algorithm, we propose a scaled Lipschitz condition which has scaling invariance. Under the condition, we estimate the iteration complexities of the proposed algorithm and provide some numerical results. The numerical results show that the algorithm is efficient and reliable. [ABSTRACT FROM AUTHOR]

This paper establishes a theoretical framework of infeasible Mehrotra-type predictor–corrector algorithm for nonmonotone nonlinear complementarity problems over symmetric cones which can be regarded as an extension the Mehrotra’s algorithm proposed by Salahi et al. (On Mehrotra-type predictor–corrector algorithms. SIAM J Optim 18(4):1377–1397, 2005) from nonnegative orthant to symmetric cone. The iteration complexity of the algorithm is estimated, and some numerical results are provided. The numerical results show that the algorithm is efficient and reliable. [ABSTRACT FROM AUTHOR]

This paper introduces a tilt integral derivative controller as the supplementary controller for load frequency control of a two-area interconnected power system. The optimal value of parameters of the tilt integral derivative controller is evaluated using constrained nonlinear optimization by means of a performance index-based method. The proposed tilt integral derivative control offers superior properties such as simple parameter tuning and its performance does not compromise the occurrence of any parameter variations in the system. To verify these features of the controller, the test system is subjected to step load disturbance and parameter variations that ensure the robustness of the tilt integral derivative controller. Comparative analysis with previously published work indicates that the proposed tilt integral derivative controller gives better performance and holds the property of robustness. Simulations have been performed using Matlab®. [ABSTRACT FROM AUTHOR]

Nonlinear complementarity and mixed complementarity problems arise in mathematical models describing several applications in Engineering, Economics and different branches of physics. Previously, robust and efficient feasible directions interior point algorithm was presented for nonlinear complementarity problems. In this paper, it is extended to mixed nonlinear complementarity problems. At each iteration, the algorithm finds a feasible direction with respect to the region defined by the inequality conditions, which is also monotonic descent direction for the potential function. Then, an approximate line search along this direction is performed in order to define the next iteration. Global and asymptotic convergence for the algorithm is investigated. The proposed algorithm is tested on several benchmark problems. The results are in good agreement with the asymptotic analysis. Finally, the algorithm is applied to the elastic-plastic torsion problem encountered in the field of Solid Mechanics. [ABSTRACT FROM AUTHOR]