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We consider composite minimization problem of the form minx h(c(x)), where the function c : Rn ! Rm is smooth and the function h : Rm ! [+1;1] is usually convex or prox-regular, but may be nonsmooth. A wide variety of important optimization problems fall into this framework, and so far several studies have been done in this regard. One of these studies relates to the condition that the function h is finite convex and the algorithm uses a line search method. Another case is solving nonlinear programming problems using a penalty function where the function h is finite polyhedral. Research has also been done for the case where the function c is identity, that is c(x) = x.We describe an... 

With the increasingly collected biological data, appropriate usage of this data is of great importance for understanding and predicting biological systems and has been the aim of experiments and data collections. A famous category of biological data is known as “omics” which refers to transcriptomics, proteomics, metabolomics, and fluxomics, from different cells or tissues in various media and conditions. This set of data is regularly used for tasks such as studying cells and organisms, understanding cell states, cancer prediction, etc. and is of great importance in Systems Biology.In this thesis, we concentrate on studying cells or organisms using such data, where during that process, we...