Convex optimization

About: Convex optimization is a research topic. Over the lifetime, 24906 publications have been published within this topic receiving 908795 citations. The topic is also known as: convex optimisation.

Clustered Multi-Task Learning: A Convex Formulation

Abstract: In multi-task learning several related tasks are considered simultaneously, with the hope that by an appropriate sharing of information across tasks, each task may benefit from the others. In the context of learning linear functions for supervised classification or regression, this can be achieved by including a priori information about the weight vectors associated with the tasks, and how they are expected to be related to each other. In this paper, we assume that tasks are clustered into groups, which are unknown beforehand, and that tasks within a group have similar weight vectors. We design a new spectral norm that encodes this a priori assumption, without the prior knowledge of the partition of tasks into groups, resulting in a new convex optimization formulation for multi-task learning. We show in simulations on synthetic examples and on the IEDB MHC-I binding dataset, that our approach outperforms well-known convex methods for multi-task learning, as well as related non-convex methods dedicated to the same problem.

Energy-Efficient Resource Allocation for Downlink Non-Orthogonal Multiple Access Network

Abstract: Non-orthogonal multiple access (NOMA) is a promising technique for the fifth generation mobile communication due to its high spectral efficiency. By applying superposition coding and successive interference cancellation techniques at the receiver, multiple users can be multiplexed on the same subchannel in NOMA systems. Previous works focus on subchannel assignment and power allocation to achieve the maximization of sum rate; however, the energy-efficient resource allocation problem has not been well studied for NOMA systems. In this paper, we aim to optimize subchannel assignment and power allocation to maximize the energy efficiency for the downlink NOMA network. Assuming perfect knowledge of the channel state information at base station, we propose a low-complexity suboptimal algorithm, which includes energy-efficient subchannel assignment and power proportional factors determination for subchannel multiplexed users. We also propose a novel power allocation across subchannels to further maximize energy efficiency. Since both optimization problems are non-convex, difference of convex programming is used to transform and approximate the original non-convex problems to convex optimization problems. Solutions to the resulting optimization problems can be obtained by solving the convex sub-problems iteratively. Simulation results show that the NOMA system equipped with the proposed algorithms yields much better sum rate and energy efficiency performance than the conventional orthogonal frequency division multiple access scheme.

Primal-Dual Splitting Algorithm for Solving Inclusions with Mixtures of Composite, Lipschitzian, and Parallel-Sum Type Monotone Operators

Abstract: We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the Lipschitzian operators present in the formulation can be processed individually via explicit steps, while the set-valued operators are processed individually via their resolvents. In addition, the algorithm is highly parallel in that most of its steps can be executed simultaneously. This work brings together and notably extends various types of structured monotone inclusion problems and their solution methods. The application to convex minimization problems is given special attention.

Control with random communication delays via a discrete-time jump system approach

Abstract: Digital control systems with random but bounded delays in the feedback loop can be modeled as finite-dimensional, discrete-time jump linear systems, with the transition jumps being modeled as finite-state Markov chains. This type of system can be called a "stochastic hybrid system". Due to the structure of the augmented state-space model, control of such a system is an output feedback problem, even if a state feedback law is intended for the original system. We present a V-K iteration algorithm to design switching and non-switching controllers for such systems. This algorithm uses an outer iteration loop to perturb the transition probability matrix. Inside this loop, one or more steps of V-K iteration is used to do controller synthesis, which requires the solution of two convex optimization problems constrained by LMIs.