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Computational optimization forms an integrated part of modern computational science.
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These optimal design problems can be reformulated as convex optimization form as the second-order cone programming and solved efficiently via the well-established interior point method.
Modelling, simulation and optimization form an integrated part of modern design practice in engineering and industry.
In this paper, we combine Rank-SVM with CVM to construct a novel SVM-type multi-label classifier (Rank-CVM) which is described as the same optimization form as binary CVM.
The optimization form is NP-Hard.
Note that the equivalence relation implies that the weighted sum-rate can be replaced with a optimization form with some additional auxiliary variables, see (14).
In the decision form – which is considered less difficult - as it is NP-Complete the question is: Can an objective value of at least K be achieved without exceeding a specific weight W? The optimization form of the problem – which is the form we try to solve in this work - tries to optimize the possible objective value.
We first put forward a linear Markov model incorporating network sparsity control and prior network information, which can be shown in the following optimization form: (1.3) min W ∑ obs = 1 ob s max ∑ k = 1 k max W x ¯ k obs − x k + 1 obs 2 + α W 1 + β W ∘ W 0 1, where obsmax represents the number of observations.
Accordingly, the proposed ductile fracture criterion is recommended for the prediction of ductile fracture in sheet metal forming processes, optimization of forming parameters and design of tools for both solid elements and shell elements.
When joined to a stipulated neighborhood diagraph, an objective functin defined on the solution space of a real combinatorial optimization problem forms a landscape.
In production engineering, there are several applications where the geometry of a designed workpiece has to be modified, e.g., optimization of forming tools during springback compensation in sheet metal forming.
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