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Application of methods of feasible directions to structural optimization problems
Computers & Structures, 1983Abstract A general approach to structural optimization which has received much attention in recent years is that of using mathematical programming (numerical search) techniques. These techniques may be separated into direct and indirect methods. Of the direct methods of attack on general nonlinear inequality constrained problems, the largest class is
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Methods of feasible directions with increased gradient memory
2005The class of feasible directions methods is a powerful tool for solving constrained minimization problems, min-max problems, and unconstrained minimization problems in the absence of continuity of the gradient. The different versions proposed either involve all the gradients and do not require "antizigzagging precautions" or involve only the ...
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Asymptotic Rates of Convergence of SQP-Type Methods of Feasible Directions
2001A modified SQP-type MFD was presented by Chen and Kostreva and its global convergence under rather mild assumptions has been proved. The numerical results showed that this modified MFD converges faster than Piron-neau — Polak’s MFD and Cawood — Kostreva’s norm-relaxed MFD.
Michael M. Kostreva, Xibin Chen
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A Modification of Feasible Direction Optimization Method for Handling Equality Constraints
Journal of Mechanisms, Transmissions, and Automation in Design, 1988The Feasible Direction Method of Zoutendijk has proven to be one of the most efficient algorithms currently available for solving nonlinear programming problems with only inequality type constraints. Since in the case of equality type constraints, there exists no nonzero direction close to the feasible region, the traditional algorithm cannot work ...
Yong Chen, Bailin Li
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The method of feasible directions for mathematical programming problems with preconvex constraints
Computational Mathematics and Mathematical Physics, 2008Summary: The convergence of the method of feasible directions is proved for the case of the smooth objective function and a constraint in the form of the difference of convex sets (the so-called preconvex set). It is shown that the method converges to the set of stationary points, which generally is narrower than the corresponding set in the case of a ...
Zabotin, V. I., Minnibaev, T. F.
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Method of Feasible Directions for Design Optimization of Gamma Irradiation Facilities
Isotopenpraxis Isotopes in Environmental and Health Studies, 1989The method of feasible directions is applied to solve some design optimization problems of gamma irradiation facilities and is tested with an example for the two-sided irradiation of a cubic container by one source. A standard mathematical program on the basis of Zoutendijek-algorithm, implemented on a 16 bit personal computer is used.
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The Efficiency of a Method of Feasible Directions for Solving Variational Inequalities
1987An algorithm of the type of feasible directions is described efficiently solving extremal problems which arise by discretization of variational inequalities. Using the maximum principle, the convergence of the method and the independence of the iteration number from the discretization parameter is shown.
H. Kirsten, R. Tichatschke
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Journal of Soviet Mathematics, 1988
The author proposes an extension of the feasible direction method for the convex programming problem: \(\min \{f^ 0(x)\), \(x\in D\}\), where \(D=\{x\in {\mathbb{R}}^ n\), \(f_ j(x)\leq 0\), \(j\in J\}\), \(J=\{1,...,m\}\). The extension is as follows. (0) Choose \(\epsilon_ 0>0\), \(\beta\in (0,1)\), \(p>0\), \(q>0.\) (1) Find \(x_ 0\in D\), set \(k=0\
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The author proposes an extension of the feasible direction method for the convex programming problem: \(\min \{f^ 0(x)\), \(x\in D\}\), where \(D=\{x\in {\mathbb{R}}^ n\), \(f_ j(x)\leq 0\), \(j\in J\}\), \(J=\{1,...,m\}\). The extension is as follows. (0) Choose \(\epsilon_ 0>0\), \(\beta\in (0,1)\), \(p>0\), \(q>0.\) (1) Find \(x_ 0\in D\), set \(k=0\
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A Method of Feasible Direction with FEM for Shape Optimization
1988The avoidance of cracks in zones of stress concentrations by minimizing the maximal von Mises stress is very important in practical problems for the industry. In many applications it is necessary to allow for the change of traction vectors in large time intervals.
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