Inexact Block Coordinate Descent Algorithms for Nonsmooth Nonconvex Optimization

In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original optimization problem with respect to that block variable. More precisely, a local approximation of the original optimization problem is solved. The proposed algorithm has several attractive features, namely, i) high flexibility, as the approximation function only needs to be strictly convex and it does not have to be a global upper bound of the original function; ii) fast convergence, as the approximation function can be designed to exploit the problem structure at hand and the stepsize is calculated by the line search; iii) low complexity, as the approximation subproblems are much easier to solve and the line search scheme is carried out over a properly constructed differentiable function; iv) guaranteed convergence of a subsequence to a stationary point, even when the objective function does not have a Lipschitz continuous gradient. Interestingly, when the approximation subproblem is solved by a descent algorithm, convergence of a subsequence to a stationary point is still guaranteed even if the approximation subproblem is solved inexactly by terminating the descent algorithm after a finite number of iterations. These features make the proposed algorithm suitable for large-scale problems where the dimension exceeds the memory and/or the processing capability of the existing hardware. These features are also illustrated by several applications in signal processing and machine learning, for instance, network anomaly detection and phase retrieval

Converting some global optimization problems to mixed integer linear problems using piecewise linear approximations

Some global optimization problems are converted to mixed-integer linear problems (MILP) using piecewise-linear approximations in this thesis so that they can be solved using commercial MILP solvers, such as CPLEX. Special attention is given to approximating two-term log-sum functions, which appears frequently in generalized geometric programming problems. Numerical results indicate the proposed approach is sound and efficient --Abstract, page iii

Waveform Optimization for Large-Scale Multi-Antenna Multi-Sine Wireless Power Transfer

Wireless power transfer (WPT) is expected to be a technology reshaping the landscape of low-power applications such as the Internet of Things, machine-to-machine communications and radio frequency identification networks. Although there has been some progress towards multi-antenna multi-sine WPT design, the large-scale design of WPT, reminiscent of massive multiple-input multiple-output (MIMO) in communications, remains an open problem. Considering the nonlinear rectifier model, a multiuser waveform optimization algorithm is derived based on successive convex approximation (SCA). A lower-complexity algorithm is derived based on asymptotic analysis and sequential approximation (SA). It is shown that the difference between the average output voltage achieved by the two algorithms can be negligible provided the number of antennas is large enough. The performance gain of the nonlinear model based design over the linear model based design can be large, in the presence of a large number of tones.Comment: To appear in the 17th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC 2016