We propose to develop mathematical models, theory, optimization algorithms and software to accelerate the integrative analysis of high-dimensional data (big data) with computational models in the field of molecular systems biology. A molecular systems approach to biology is characterized by an iterative process. Initially, a computational model is built from available experimental data to predict the behavior of a particular biological system based on the current understanding of the underlying molecular mechanisms. New experimental data is then generated to test and refine the model so that the next prediction more accurately predicts behavior of the system. Over the past two decades, advances in both experimental technologies and biochemical network reconstruction and have led to an exponential growth in the dimensions of experimental data and computational models derived from reconstruction efforts. Here, the dimension is the number of different molecular species quantified using an experimental approach or the number of different biochemical reactions modeled in a biological system of interest, which need to be matched for integrative analysis of data in the context of a model. Constraint-based reconstruction and analysis has become the dominant approach for generation of mechanistic predictions from genome-scale biochemical networks because the underlying computational approach is based on default application of generic optimization software with worst case time-complexity that scales polynomially with the dimension of the model. While this approach has been successful for models up to approximately 1e4 variables, by the end of this year we will have models with almost 1e7 variables, and with even higher dimensional models envisaged. We propose to develop mathematically and numerically sophisticated approaches to better exploit the capacity of existing optimization software to model most of the existing real-world biological networks and develop novel globally convergent and computationally efficient optimization methods that are tailored for the largest existing and emerging big data problems in molecular systems biology. The theoretical and numerical foundations gained will be disseminated by standard academic methods and also by establishment of a Luxembourgish Optimization Facility where scientists will be trained to exploit the most appropriate optimization software on high performance computing resources at the University of Luxembourg.