ISSN:

2155-3289

eISSN:

2155-3297

## Numerical Algebra, Control & Optimization

June 2021 , Volume 11 , Issue 2

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**Abstract:**

The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. The controlled equations of motion are solved numerically using a predictor-corrector continuation method, starting from an initial solution obtained via a direct method, to realize trajectory tracking and obstacle avoidance maneuvers.

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**Abstract:**

In this paper we consider non-cooperative game problem based on the Malfatti's problem. This problem is a special case of generalized Nash equilibrium problems with nonconvex shared constraints. Some numerical results are provided.

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**Abstract:**

One of the challenges facing supply chain designers is designing a sustainable and resilient supply chain network. The present study considers a closed-loop supply chain by taking into account sustainability, resilience, robustness, and risk aversion for the first time. The study suggests a two-stage mixed-integer linear programming model for the problem. Further, the robust counterpart model is used to handle uncertainties. Furthermore, conditional value at risk criterion in the model is considered in order to create real-life conditions. The sustainability goals addressed in the present study include minimizing the costs,

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**Abstract:**

Regularized Multidimensional Scaling with Radial basis function (RMDS) is a nonlinear variant of classical Multi-Dimensional Scaling (cMDS). A key issue that has been addressed in RMDS is the effective selection of centers of the radial basis functions that plays a very important role in reducing the dimension preserving the structure of the data in higher dimensional space. RMDS uses data in unsupervised settings that means RMDS does not use any prior information of the dataset. This article is concerned on the supervised setting. Here we have incorporated the class information of some members of data to the RMDS model. The class separability term improved the method RMDS significantly and also outperforms other discriminant analysis methods such as Linear discriminant analysis (LDA) which is documented through numerical experiments.

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**Abstract:**

We apply a space adaptive interior penalty discontinuous Galerkin method for solving advective Allen-Cahn equation with expanding and contracting velocity fields. The advective Allen-Cahn equation is first discretized in time and the resulting semi-linear elliptic PDE is solved by an adaptive algorithm using a residual-based a posteriori error estimator. The a posteriori error estimator contains additional terms due to the non-divergence-free velocity field. Numerical examples demonstrate the effectiveness and accuracy of the adaptive approach by resolving the sharp layers accurately.

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**Abstract:**

There are a limited number of user-friendly, publicly available optimal control software packages that are designed to accommodate problems with delays. GPOPS-Ⅱ is a well developed MATLAB based optimal control code that was not originally designed to accommodate problems with delays. The use of GPOPS-Ⅱ on optimal control problems with delays is examined for the first time. The use of various formulations of delayed optimal control problems is also discussed. It is seen that GPOPS-Ⅱ finds a suboptimal solution when used as a direct transcription delayed optimal control problem solver but that it is often able to produce a good solution of the optimal control problem when used as a delayed boundary value solver of the necessary conditions.

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**Abstract:**

A singularly perturbed linear time-dependent controlled system with a point-wise nonsmall (of order of

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**Abstract:**

In a grid network, the nodes could be traversed either horizontally or vertically. The constrained shortest Hamiltonian path goes over the nodes between a source node and a destination node, and it is constrained to traverse some nodes at least once while others could be traversed several times. There are various applications of the problem, especially in routing problems. It is an NP-complete problem, and the well-known Bellman-Held-Karp algorithm could solve the shortest Hamiltonian circuit problem within

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