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Comparison of Algorithms for Automatic Creation of Virtual Manikin Motions
Published in Vincent G. Duffy, Advances in Applied Human Modeling and Simulation, 2012
Niclas Delfs, Robert Bohlin, Peter MåRdberg, Stefan Gustafsson, Johan S. Carlson
The term interior point method is used to describe any method solving a sequence of unconstrained minimization problem using a decreasing multiplier μ to find a local solution within the interior of the feasible region of the problem (Doyle 2003). The problem (4.1) would then be minimize-h(x)-μk∑i=1mlnμk-gi(x)
A Dynamical Systems Approach to Solving Linear Programming Problems
Published in K. D. Elworthy, W. Norrie Evenitt, E. Bruce Lee, Differential equations, dynamical systems, and control science, 2017
Stanislaw H. Zak, Viriya Upatising, Walter E. Lillo, Stefen Hui
Linear programming (LP) plays a fundamental role in many disciplines such as economics, strategic planning, analysis of algorithms, combinatorial problems, etc. In 1947, Dantzig ([1]) developed a method for solving linear programs which is known today as the simplex method. In 1951, Brown and Koopmans ([2]) described the first of a series of interior point methods for solving linear programs. Khachiyan ([3]) showed that linear programming problems can be solved in polynomial time using his ellipsoid method (see [4] for a discussion of this technique). However, computational experience with the ellipsoid algorithm has shown that it is not a practical alternative to the simplex method ([5, 6]). Recently, Karmarkar ([7]) (see also Strang ([8]) or Schrijver ([4]) for more details of this method) developed a linear programming algorithm which solves some complicated real-world problems of scheduling, routing and planning more efficiently than the simplex method. The simplex method is classified as an exterior point method and Karmarkar's method is classified as an interior point method ([9]). Recently, Gill et al. ([6]) showed that the whole family of the interior point methods can be derived from some classical results from the field of nonlinear programming. The classical methods of nonlinear programming include the penalty function method ([10]) and the barrier method ([11]). Conn ([12]) developed alternative methods for solving linear programs utilizing unconstrained optimization with penalty function methods. Another approach to solving LP problems, using interconnected networks of simple analog processors, was proposed by Pyne ([13]) and later studied by Rybashov ([14, 15]), Karpinskaya ([16]), and others. Since then various dynamic LP problem solvers have been proposed - see e.g. Tank and Hopfield ([17]), Kennedy and Chua ([18]), Rodriguez-Vazquez et al. ([19]), and Cichocki and Unbehauen ([20]).
Family learning: A process modeling method for cyber-additive manufacturing network
Published in IISE Transactions, 2021
Lening Wang, Xiaoyu Chen, Daniel Henkel, Ran Jin
For the optimization problem can be efficiently solved by use of the interior-point method (Mehrotra, 1992; Forsgren et al.,2002). The interior-point method is an efficient optimization method for both linear and nonlinear problems. The optimization problem for is a convex problem (Zhou et al.,2011), and can be efficiently solved via accelerated gradient descent (Nesterov, 2007; Chen et al., 2009). By adding Nesterov’s momentum term, the accelerated gradient descent can balance the gradient updates and an appropriate extrapolation for optimization at nearly the same cost assocites with ordinary gradient descent. To select the optimal tuning parameters and five-fold cross-validation is employed. In five-fold cross-validation, first, the whole training dataset is randomly separated into five subsets with an almost equal number of samples. Then, four out of five subsets are used for training, and the remaining one is used to validate the model. The cross-validation process is then repeated five times, with each of the five subsets used exactly once as the validation set. Based on the performance of the model under different tuning parameters, the best combination of tuning parameters is selected (Tibshirani et al., 2005). The Root-Mean-Squared Error (RMSE) obtained in the cross-validation process is used to select the two tuning parameters.
Practical Framework for Self-healing of Smart Grids in Stable/Unstable Power Swing Conditions
Published in Electric Power Components and Systems, 2012
N. Moaddabi, S. H. Hosseinian, G. B. Gharehpetian
In general, there is no analytical formula for the solution of convex optimization problems, but (as with linear programming problems) there are very effective methods for solving them. Interior-point methods work very well in practice and, in some cases, can be proved to solve the problem to a specified accuracy with a number of operations that does not exceed a polynomial of the problem dimensions. The interior-point methods can solve the problem in Eq. (9) in a number of steps or iterations that is usually in the range between 10 and 100. Like other methods for solving linear programming problems, these interior-point methods are quite reliable. The problems with hundreds of variables and thousands of constraints can be solved easily on a current desktop computer, in at most a few tens of seconds. By exploiting problem structure (such as sparsity), far larger problems can be solved that have many thousands of variables and constraints [16].
Generation Rescheduling Based Contingency Constrained Optimal Power Flow Considering Uncertainties Through Stochastic Modeling
Published in IETE Journal of Research, 2023
Mohammad Nasir, Ali Sadollah, Hassan Barati, Mona Khodabakhshi, Joong Hoon Kim
In Ref. [3], the fuzzy control approach has been introduced through active generation rescheduling in order to relieve the transmission lines overload. Further, the diverse classical optimization methods have been developed to solve the OPF problem, such as the gradient method [4], Newton method [5], decoupling technique [6], and the interior point method [7]. However, the gradient method has poor convergence characteristics, whereas the Newton method is bounded to continuity of the problem definition and constraints. The interior point method is time consuming and converges to local optimum. Hence, the classical techniques suffer from several weaknesses to acquire the OPF solution.