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In this article, a generalization of the αECP algorithm to cover a class of nondifferentiable Mixed-Integer NonLinear Programming problems is studied. In the generalization constraint functions are required to be f • -pseudoconvex instead of pseudoconvex functions. This enables the functions to be nonsmooth. The objective function is first assumed to be linear but also f • -pseudoconvex case is considered. Furthermore, the gradients used in the αECP algorithm are replaced by the subgradients of Clarke subdifferential. With some additional assumptions, the resulting algorithm shall be proven to converge to a global minimum.

Recent technological developments in genetic screening approaches have offered the means to start exploring quantitative genotype-phenotype relationships on a large-scale. What remains unclear is the extent to which the quantitative genetic interaction datasets can distinguish the broad spectrum of interaction classes, as compared to existing information on mutation pairs associated with both positive and negative interactions, and whether the scoring of varying degrees of such epistatic effects could be improved by computational means. To address these questions, we introduce here a computational approach for improving the quantitative discrimination power encoded in the genetic interaction screening data. Our matrix approximation model decomposes the original double-mutant fitness matrix into separate components, representing variability across the array and query mutants, which can be utilized for estimating and correcting the single-mutant fitness effects, respectively. When applied to three large-scale quantitative interaction datasets in yeast, we could improve the accuracy of scoring various interaction classes beyond that obtained with the original fitness data, especially in synthetic genetic array (SGA) and in genetic interaction mapping (GIM) datasets. In addition to the known pairs of interactions used in the evaluation of the computational approach, a number of novel interaction pairs were also predicted, along with underlying biological mechanisms, which remained undetected by the original datasets. It was shown that the optimal choice of the scoring function depends heavily on the screening approach and on the interaction class under analysis. Moreover, a simple preprocessing of the fitness matrix could further enhance the discrimination power of the epistatic miniarray profiling (E-MAP) dataset. These systematic evaluation results provide in-depth information on the optimal analysis of the future, large-scale screening experiments. In general, the modeling framework, enabling accurate identification and classification of genetic interactions, provides a solid basis for completing and mining the genetic interaction networks in yeast and other organisms.

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