We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lo...

Convex 1-D first-order total variation (TV) denoising is an effective method for eliminating signal noise, which can be defined as convex optimization consisting of a quadratic data fidelity term and a non-convex regularization term. It not only ensures strict convex for optimization problems, but also improves the sparseness of the total variation term by introducing the non-convex penalty fun...

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. As direct rank minimization is NP hard, many alternative choices have been proposed. In this survey, we first introduce optimization approaches for two popular methods on rank minimization, i.e., nuclear norm regularization and rank constraint. Nuclear norm is the tightest con...

Cooperative communication and orthogonal frequency division multiplexing (OFDM) technology are both promising candidates for next generation wireless communication systems. In this paper a Linear Programming (LP) based subcarrier allocation algorithm for cooperative multiuser OFDM system with grouped user is proposed. The proposed algorithm maximizes the data rate of all users over downlink und...

In this paper a new method is introduced for path planning of an autonomous vehicle. In this method, the environment is considered cluttered and with some uncertainty sources. Thus, the state of detected object should be estimated using an optimal filter. To do so, the state distribution is assumed Gaussian. Thus the state vector is estimated by a Kalman filter at each time step. The estimation...

The dose-volume histogram (DVH) is a clinically relevant criterion to evaluate the quality of a treatment plan. It is hence desirable to incorporate DVH constraints into treatment plan optimization for intensity modulated radiation therapy. Yet, the direct inclusion of the DVH constraints into a treatment plan optimization model typically leads to great computational difficulties due to the non...

Online convex optimization is a sequential prediction framework with the goal to track and adapt to the environment through evaluating proper convex loss functions. We study efficient particle filtering methods from the perspective of such framework. We formulate an efficient particle filtering methods for non-stationary environment by making connections with the online mirror descent algorithm...

In this thesis, we study the downlink multiuser scheduling and power allocation problem for systems with simultaneous wireless information and power transfer (SWIPT). In the first part of the thesis, we focus on multiuser scheduling. We design optimal scheduling algorithms that maximize the long-term average system throughput under different fairness requirements, such as proportional fairness ...

We propose a localized approach to multiple kernel learning that can be formulated as a convex optimization problem over a given cluster structure. For which we obtain generalization error guarantees and derive an optimization algorithm based on the Fenchel dual representation. Experiments on real-world datasets from the application domains of computational biology and computer vision show that...