In this thesis, a novel successive convexification scheme is proposed for solving consistent labeling problems with convex regularization terms. Many computer vision problems can be modeled as such consistent labeling problems. The main optimization term, the labeling cost, however, is typically non-convex, which makes the problem difficult. As well, the large search space, i.e., formally the l...

We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger conv...

Maximizing the sum rates in a multiuser Gaussian channel by power control is a nonconvex NP-hard problem that finds engineering application in code division multiple access (CDMA) wireless communication network. In this paper, we extend and apply several fundamental nonnegative matrix inequalities initiated by Friedland and Karlin in a 1975 paper to solve this nonconvex power control optimizati...

We know that the same set of selected extrema can be represented by a large number of different monotonicity graphs. We are interested in understanding how different, or how similar, the converged reconstruction results can be with respect to different monotonicity graphs. To do so, we made the following experiment. We constructed 100 random monotonicity graphs for the 2D vorticity data set (Fi...

System identification studies how to construct mathematical models for dynamical systems from the input and output data, which finds applications in many scenarios, such as predicting future output of the system or building model based controllers for regulating the output the system. Among many other methods, convex optimization is becoming an increasingly useful tool for solving system identi...

Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a mixed integer program (MIP) whose objective function is non-convex. In this form, the problem is resistant to standard optimization techniques. We construct MIP...