This paper gives an overview of the majorization-minimization (MM) algorithmic framework, which can provide guidance in deriving problem-driven algorithms with low computational cost. A general introduction of MM is presented, including a description of the basic principle and its convergence results. The extensions, acceleration schemes, and connection to other algorithmic frameworks are also covered. To bridge the gap between theory and practice, upperbounds for a large number of basic functions, derived based on the Taylor expansion, convexity, and special inequalities, are provided as ingredients for constructing surrogate functions. With the pre-requisites established, the way of applying MM to solving specific problems is elaborated by a wide range of applications in signal processing, communications, and machine learning.

Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning

In this paper, we investigate resource allocation algorithm design for multicarrier non-orthogonal multiple access (MC-NOMA) systems employing a full-duplex (FD) base station for serving multiple half-duplex (HD) downlink and uplink users simultaneously. The proposed algorithm is obtained from the solution of a non-convex optimization problem for the maximization of the weighted sum system throughput. We apply monotonic optimization to develop an optimal joint power and subcarrier allocation policy. The optimal resource allocation policy serves as a system performance benchmark due to its high computational complexity. Furthermore, a suboptimal iterative scheme based on successive convex approximation is proposed to strike a balance between computational complexity and optimality. Our simulation results reveal that the proposed suboptimal algorithm achieves a close-to-optimal performance. In addition, FD MC-NOMA systems employing the proposed resource allocation algorithms provide a substantial system throughput improvement compared with conventional HD multicarrier orthogonal multiple access (MC-OMA) systems and other baseline schemes. In addition, our results unveil that FD MC-NOMA systems enable a fairer resource allocation compared with traditional HD MC-OMA systems.

Optimal Joint Power and Subcarrier Allocation for Full-Duplex Multicarrier Non-Orthogonal Multiple Access Systems

In this paper, we investigate the resource allocation algorithm design for multicarrier solar-powered unmanned aerial vehicle (UAV) communication systems. In particular, the UAV is powered by the solar energy enabling sustainable communication services to multiple ground users. We study the joint design of the 3D aerial trajectory and the wireless resource allocation for maximization of the system sum throughput over a given time period. As a performance benchmark, we first consider an off-line resource allocation design assuming non-causal knowledge of the channel gains. The algorithm design is formulated as a mixed-integer non-convex optimization problem taking into account the aerodynamic power consumption, solar energy harvesting, a finite energy storage capacity, and the quality-of-service requirements of the users. Despite the non-convexity of the optimization problem, we solve it optimally by applying monotonic optimization to obtain the optimal 3D-trajectory and the optimal power and subcarrier allocation policy. Subsequently, we focus on the online algorithm design that only requires real-time and statistical knowledge of the channel gains. The optimal online resource allocation algorithm is motivated by the off-line scheme and entails a high computational complexity. Hence, we also propose a low-complexity iterative suboptimal online scheme based on the successive convex approximation. Our simulation results reveal that both the proposed online schemes closely approach the performance of the benchmark off-line scheme and substantially outperform two baseline schemes. Furthermore, our results unveil the tradeoff between solar energy harvesting and power-efficient communication. In particular, the solar-powered UAV first climbs up to a high altitude to harvest a sufficient amount of solar energy and then descends again to a lower altitude to reduce the path loss of the communication links to the users it serves.

Optimal 3D-Trajectory Design and Resource Allocation for Solar-Powered UAV Communication Systems

In this paper, we study power-efficient resource allocation for multicarrier non-orthogonal multiple access systems. The resource allocation algorithm design is formulated as a non-convex optimization problem which jointly designs the power allocation, rate allocation, user scheduling, and successive interference cancellation (SIC) decoding policy for minimizing the total transmit power. The proposed framework takes into account the imperfection of channel state information at transmitter and quality of service requirements of users. To facilitate the design of optimal SIC decoding policy on each subcarrier, we define a channel-to-noise ratio outage threshold . Subsequently, the considered non-convex optimization problem is recast as a generalized linear multiplicative programming problem, for which a globally optimal solution is obtained via employing the branch-and-bound approach. The optimal resource allocation policy serves as a system performance benchmark due to its high computational complexity. To strike a balance between system performance and computational complexity, we propose a suboptimal iterative resource allocation algorithm based on difference of convex programming. Simulation results demonstrate that the suboptimal scheme achieves a close-to-optimal performance. Also, both proposed schemes provide significant transmit power savings than that of conventional orthogonal multiple access schemes.

Optimal Resource Allocation for Power-Efficient MC-NOMA With Imperfect Channel State Information

In this paper, we investigate the resource allocation algorithm design for multicarrier solar-powered unmanned aerial vehicle (UAV) communication systems. In particular, the UAV is powered by solar energy enabling sustainable communication services to multiple ground users. We study the joint design of the three-dimensional (3D) aerial trajectory and the wireless resource allocation for maximization of the system sum throughput over a given time period. As a performance benchmark, we first consider an offline resource allocation design assuming non-causal knowledge of the channel gains. The algorithm design is formulated as a mixed-integer non-convex optimization problem taking into account the aerodynamic power consumption, solar energy harvesting, a finite energy storage capacity, and the quality-of-service (QoS) requirements of the users. Despite the non-convexity of the optimization problem, we solve it optimally by applying monotonic optimization to obtain the optimal 3D-trajectory and the optimal power and subcarrier allocation policy. Subsequently, we focus on online algorithm design which only requires real-time and statistical knowledge of the channel gains. The optimal online resource allocation algorithm is motivated by the offline scheme and entails a high computational complexity. Hence, we also propose a low-complexity iterative suboptimal online scheme based on successive convex approximation. Our results unveil the tradeoff between solar energy harvesting and power-efficient communication. In particular, the solar-powered UAV first climbs up to a high altitude to harvest a sufficient amount of solar energy and then descents again to a lower altitude to reduce the path loss of the communication links to the users it serves.

This paper introduces sequential convex programming (SCP), a local optimzation method for solving nonconvex optimization problems. A full-step SCP algorithm is presented. Under mild conditions the local convergence of the algorithm is proved as a main result of this paper. An application to optimal control illustrates the performance of the proposed algorithm.

Local Convergence of Sequential Convex Programming for Nonconvex Optimization

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time. In the case of a robotic manipulator with simplified constraints, a convex reformulation of this optimal control problem has been derived previously. However, many applications in robotics feature constraints such as velocity-dependent torque constraints or torque rate constraints that destroy the convexity. The present paper proposes an efficient sequential convex programming (SCP) approach to solve the corresponding nonconvex optimal control problems by writing the nonconvex constraints as a difference of convex (DC) functions, resulting in convex-concave constraints. We consider seven practical applications that fit into the proposed framework even when mutually combined, illustrating the flexibility and practicality of the proposed framework. Furthermore, numerical simulations for some typical applications illustrate the fast convergence of the proposed method in only a few SCP iterations, confirming the efficiency of the proposed framework.

/pdf/time-optimal-path-following-for-robots-with-convex-concave-4jeqo29nb3.pdf

Time-Optimal Path Following for Robots With Convex–Concave Constraints Using Sequential Convex Programming

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorit...

Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization

In this work, we propose a new local optimization method to solve a class of nonconvex semidefinite programming (SDP) problems. The basic idea is to approximate the feasible set of the nonconvex SDP problem by inner positive semidefinite convex approximations via a parameterization technique. This leads to an iterative procedure to search a local optimum of the nonconvex problem. The convergence of the algorithm is analyzed under mild assumptions. Applications to optimization problems with bilinear matrix inequality (BMI) constraints in static output feedback control are benchmarked and numerical tests are implemented based on the data from the COMPL e ib library.

An inner convex approximation algorithm for BMI optimization and applications in control

We propose a dual decomposition method for solving separable nonconvex optimization problems that arise e.g. in distributed model predictive control over networks. We first derive a new sequential convex programming (SCP) scheme based on penalty function approach to handle nonconvexity. Then, we combine this SCP scheme with a dual decomposition algorithm to obtain a two-level decomposition algorithm. The global convergence of this algorithm is analyzed under standard assumptions. Some preliminary numerical results are also given to illustrate the theoretical results.

Quoc Tran Dinh

Papers

Local Convergence of Sequential Convex Programming for Nonconvex Optimization

Time-Optimal Path Following for Robots With Convex–Concave Constraints Using Sequential Convex Programming

Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization

An inner convex approximation algorithm for BMI optimization and applications in control

A dual decomposition algorithm for separable nonconvex optimization using the penalty function framework