Joint Optimization for on-Demand Deployment of UAVs and Spectrum Allocation in UAVs-Assisted Communication

To improve the efficiency and fairness of the spectrum allocation for ground communication assisted by unmanned aerial vehicles(UAVs),a joint optimization method for on-demand deployment and spectrum allocation of UAVs is proposed,which is modeled as a mixed-integer non-convex optimization problem(MINCOP).An algorithm to estimate the minimum number of required UAVs is firstly proposed based on the pre-estimation and simulated annealing.The MINCOP is then decomposed into three sub-problems based on the block coordinate descent method,including the spectrum allocation of UAVs,the association between UAVs and ground users,and the deployment of UAVs.Specifically,the optimal spectrum allocation is derived based on the interference mitigation and channel reuse.The association between UAVs and ground users is optimized based on local iterated optimization.A particle-based optimization algorithm is proposed to resolve the subproblem of the UAVs deployment.Simulation results show that the proposed method could effectively improve the minimum transmission rate of UAVs as well as user fairness of spectrum allocation.

A Parallel Line Search Subspace Correction Method for Composite Convex Optimization

In this paper,we investigate a parallel subspace correction framework for composite convex optimization.The variables are first divided into a few blocks based on certain rules.At each iteration,the algorithms solve a suitable subproblem on each block simultaneously,construct a search direction by combining their solutions on all blocks,then identify a new point along this direction using a step size satisfying the Armijo line search condition.They are called PSCLN and PSCLO,respectively,depending on whether there are overlapping regions between two imme-diately adjacent blocks of variables.Their convergence is established under mild assumptions.We compare PSCLN and PSCLO with the parallel version of the fast iterative thresholding algorithm and the fixed-point continuation method using the Barzilai-Borwein step size and the greedy coordinate block descent method for solving the l1-regularized minimization problems.Our numerical results showthatPSCLN andPSCLOcan run fast and return solutions notworse than those from the state-of-theart algorithms on most test problems.It is also observed that the overlapping domain decomposition scheme is helpful when the data of the problem has certain special structures.

A Two-stage Adaptive Robust Model for Residential Micro-CHP Expansion Planning

This paper addresses the planning problem of residential micro combined heat and power (micro-CHP) systems (including micro-generation units, auxiliary boilers, and thermal storage tanks) considering the associated technical and economic factors. Since the accurate values of the thermal and electrical loads of this system cannot be exactly predicted for the planning horizon, the thermal and electrical load uncertainties are modeled using a two-stage adaptive robust optimization method based on a polyhedral uncertainty set. A solution method, which is composed of column-and-constraint generation (C&CG) algorithm and block coordinate descent (BCD) method, is proposed to efficiently solve this adaptive robust optimization model. Numerical results from a practical case study show the effective performance of the proposed adaptive robust model for residential micro-CHP planning and its solution method.

On the Linear Convergence of the Approximate Proximal Splitting Method for Non-smooth Convex Optimization

Consider the problem of minimizing the sum of two convex functions,one being smooth and the other non-smooth.In this paper,we introduce a general class of approximate proximal splitting(APS)methods for solving such minimization problems.Methods in the APS class include many well-known algorithms such as the proximal splitting method,the block coordinate descent method(BCD),and the approximate gradient projection methods for smooth convex optimization.We establish the linear convergence of APS methods under a local error bound assumption.Since the latter is known to hold for compressive sensing and sparse group LASSO problems,our analysis implies the linear convergence of the BCD method for these problems without strong convexity assumption.