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In the article a new approach for solving complex and highly nonlinear differential-algebraic equations (DAEs) was presented. An important kind of applications of DAE systems is modeling of biotechnological processes, which can have a very different course. An efficient solving of equations describing biotechnological industrial inlets results in better optimization of the processes and has a positive...
In geometric constraint solving, the constraints are represented with an equation system F(U, X) = 0, where X denotes the unknowns and U denotes a set of parameters. The target solution for X is noted XT. A witness is a couple (UW, XW) such that F(UW, XW) = 0. The witness is not the target solution, but they share the same combinatorial features, even when the witness and the target lie on two distinct...
Due to increasing computer processing power, Newton's method is receiving again increasing interest for solving optimization problems. In this paper, we provide a methodology for solving smooth norm optimization problems under some linear constraints using the Newton's method. This problem arises in many machine learning and graph optimization applications. We consider as a case study optimal weight...
Based on the smoothing NCP function, we first reformulate the generalized nonlinear complementarity problem over a polyhedral cone as a smoothing system of equations, and then propose a new smoothing inexact Newton method for solving it. In each iteration, the corresponding linear system is solved only inexact solution. Under suitable conditions, we show that any accumulation point of the generated...
In this paper a new approach to formulate the constrained Linear Quadratic Regulator (LQR) problem as a Quadratic Programming (QP) problem is introduced. The new approach takes advantage of the (Moore-Penrose) generalized inverse to eliminate control inputs as decision variables, hence the optimization is performed only over the states belonging to the prediction horizon. This allows one to save on...
The optimal production control of a flexible manufacturing system subject to random Markov disturbances is considered. The resulting optimality conditions, which are expressed as a system of stochastic partial differential equations, are analytically unsolvable for non-trivial systems. An alternative, simulation-based, numerical technique has been proposed in [2]. It uses infinitesimal perturbation...
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