Singh et al. [1], for solving the fully neutrosophic linear programming problems stated that the method of Abdel-Basset et al. [2] is scientifically incorrect and suggested a modified version for it. They have constru...
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When operating hybrid desalination plants combining multistage flash (MSF) and reverse osmosis (RO) processes, it is crucial to determine the blend ratios of water produced by these two processes. These blend ratios m...
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When operating hybrid desalination plants combining multistage flash (MSF) and reverse osmosis (RO) processes, it is crucial to determine the blend ratios of water produced by these two processes. These blend ratios must take economic and environmental aspects of the hybrid plant's sustainability into consideration, and must enable the plant to meet constraint conditions with respect to water demand, energy consumption savings, and saline content. We mathematically resolve this issue by formulating it as a linear programing problem and by computing that problem's solutions. Permissible solutions occur as an area in a triangle in the MSF-RO blend ratio diagram, and the most desirable solutions occur at (1) the intersection point between the water demand limit line and salinity limit line and at (2) the intersection point between the water demand limit line and the energy savings limit line.
We consider the problem of designing output feedback controllers that use measurements from a set of landmarks to navigate through a cell-decomposable environment using duality, control Lyapunov function and control b...
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We consider the problem of designing output feedback controllers that use measurements from a set of landmarks to navigate through a cell-decomposable environment using duality, control Lyapunov function and control barrier function, and linear programming. We propose two objectives for navigating in an environment, one to traverse the environment by making loops and one by converging to a stabilization point while smoothing the transition between consecutive cells. We test our algorithms in a simulation environment, evaluating the robustness of the approach to practical conditions, such as bearing-only measurements, and measurements acquired with a camera with a limited field of view.
This paper explores the design of an inventory management model for small warehouses using machine learning and optimization methods. The objective is to develop a system that ensures accurate demand forecasting and a...
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According to Dantzig (Econometrica, 17, p.200, 1949), von Neumann was the first to observe that for any finite two-person zero-sum game, there is a feasible linear programming (LP) problem whose saddle points yield eq...
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According to Dantzig (Econometrica, 17, p.200, 1949), von Neumann was the first to observe that for any finite two-person zero-sum game, there is a feasible linear programming (LP) problem whose saddle points yield equilibria of the game, thus providing an immediate proof of the minimax theorem from the strong duality theorem. We provide an analogous construction going in the other direction. For any LP problem, we define a game and, with a brief and elementary proof, show that every equilibrium either yields a saddle point of the LP problem or certifies that one of the primal or dual programs is infeasible and the other is infeasible or unbounded. We thus obtain an immediate proof of the strong duality theorem from the minimax theorem. Taken together, von Neumann's and our results provide a succinct and elementary demonstration that matrix games and linear programming are "equivalent" in a classical sense.
The stable roommates problem is a non-bipartite version of the well-known stable matching problem. Teo and Sethuraman proved that, for each instance of the stable roommates problem in the complete graphs, there exists...
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Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph has no cycles of odd number of negative edges. Lapl...
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ISBN:
(数字)9798350368741
ISBN:
(纸本)9798350368758
Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph has no cycles of odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map simply to ones in a similarity-transformed positive graph Laplacian, thus enabling reuse of well-studied spectral filters designed for positive graphs. We propose a fast method to learn a balanced signed graph Laplacian directly from data. Specifically, for each node i, to determine its polarity β i ∈{−1,1} and edge weights $\left\{ {{w_{i,j}}} \right\}_{j = 1}^N$, we extend a sparse inverse covariance formulation based on linear programming (LP) called CLIME, by adding linear constraints to enforce "consistent" signs of edge weights $\left\{ {{w_{i,j}}} \right\}_{j = 1}^N$ with the polarities of connected nodes—i.e., positive/negative edges connect nodes of same/opposing polarities. For each LP, we adopt projections on convex set (POCS) to determine a suitable CLIME parameter ρ > 0 that guarantees LP feasibility. We solve the resulting LP via an off-the-shelf LP solver. Experiments on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables the use of spectral filters and graph neural networks designed for positive graphs on balanced signed graphs.
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to e...
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We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute these quantities using dynamic and linear programming.
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