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Since our stated problem exhibits a clear ordering of the objectives with respect to their priority, namely junction-cleavage likelihood over neo-immunogenicity, the problem of finding a Pareto-optimal solution can be significantly simplified by applying lexicographical ordered optimization (LO).
For example, they have been applied to solve equilibrium problems for strategic games with incomplete preferences (see [3]), ordered optimization problems and ordered variational inequality problems (see [4]), nonlinear Hammerstein integral equations (see [5]) and ordinal differential equations (see [1] and [2]).
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A Hierarchical Clustering analysis on the presence/absence pattern of all CFs found in the cyanobacterial genomes was done using the MeV software (v4.8; http://mev-tm4.sourceforge.net) and the following parameters: Pearson correlation, ordering optimization on the species, average linkage clustering.
We illustrate the relative merits and performance of quasi-Newton and full second-order optimization with a series of examples, showing that even a pulse already optimized using other methods can be visibly improved.
Then, random method and first-order optimization method were applied in the optimization process.
During the subsequent interaction order optimization, the method tries to find an order, which satisfies this adjacency demand.
Migration of the proposed method to higher-order optimization domains bears a big promise and requires further research.
SOPs include linear optimization problems, semidefinite optimization problems, second-order optimization problems, and various combinations of these types of problems as special cases.
In this paper, we introduce a stochastic, zero-order optimization algorithm based on the principles of learning.
A first order optimization method is adopted for that purpose while the gradients required are efficiently derived analytically.
To overcome its high computational cost and make it applicable for optimization of large-scale structures, a novel reduced-order optimization algorithm is proposed.
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