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.

Design of variable–stiffness laminates using lamination parameters

Abstract: Benefits of the directional properties of fiber reinforced composites could be fully utilized by proper placement of the fibers in their optimal spatial orientations. This paper investigates the optimal design of fiber reinforced rectangular composite plates for minimum compliance. The classical minimum compliance design problem is formulated in the lamination parameters space. The use of lamination parameters guarantees that the obtained solutions represent the best possible performance of the structure since there are no restrictions on the possible lamination sequence. Two types of designs are considered: constant–stiffness designs where the lamination parameters are constant over the plate domain, and variable-stiffness designs where the laminations parameters are allowed to vary in a continuous manner over the domain. The optimality conditions for the problem are reformulated as a local design rule. The local design rule assumes the form of a convex optimization problem and is solved using a feasible sequential quadratic programming. Optimal designs for both constant and variable–stiffness plates are obtained. It is shown that significant improvements in stiffness can be gained by using variable–stiffness design.

Verification of linear hybrid systems by means of convex approximations

Abstract: We present a new application of the abstract interpretation by means of convex polyhedra, to a class of hybrid systems, i.e., systems involving both discrete and continuous variables. The result is an efficient automatic tool for approximate, but conservative, verification of reachability properties of these systems.

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

Abstract: 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.

Secure communication over MISO cognitive radio channels

Abstract: In this paper, we address the physical-layer security issue of a secondary user (SU) in a spectrum-sharing cognitive radio network (CRN) from an information-theoretic perspective. Specially, we consider a secure multiple-input single-output (MISO) cognitive radio channel, where a multi-antenna SU transmitter (SU-Tx) sends confidential information to a legitimate SU receiver (SU-Rx) in the presence of an eavesdropper and on the licensed band of a primary user (PU). The secrecy capacity of the channel is characterized, which is a quasiconvex optimization problem of finding the capacity-achieving transmit covariance matrix under the joint transmit power and interference power constraints. Two numerical approaches are proposed to derive the optimal transmit covariance matrix. The first approach recasts the original quasiconvex problem into a single convex semidefinite program (SDP) by exploring its inherent convexity; while the second one explores the relationship between the secure CRN and the conventional CRN and transforms the original problem into a sequence of optimization problems associated with the conventional CRN, which helps to prove that beamforming is the optimal strategy for the secure MISO CR channel. In addition, to reduce the computational complexity, three suboptimal schemes are presented, namely, scaled secret beamforming (SSB), projected secret beamforming (PSB) and projected cognitive beamforming (PCB). Lastly, computer simulation results show that the three suboptimal schemes can approach the secrecy capacity well under certain conditions.

Lossless Convexification of Nonconvex Control Bound and Pointing Constraints of the Soft Landing Optimal Control Problem

Abstract: Planetary soft landing is one of the benchmark problems of optimal control theory and is gaining renewed interest due to the increased focus on the exploration of planets in the solar system, such as Mars. The soft landing problem with all relevant constraints can be posed as a finite-horizon optimal control problem with state and control constraints. The real-time generation of fuel-optimal paths to a prescribed location on a planet's surface is a challenging problem due to the constraints on the fuel, the control inputs, and the states. The main difficulty in solving this constrained problem is the existence of nonconvex constraints on the control input, which are due to a nonzero lower bound on the control input magnitude and a nonconvex constraint on its direction. This paper introduces a convexification of the control constraints that is proven to be lossless; i.e., an optimal solution of the soft landing problem can be obtained via solution of the proposed convex relaxation of the problem. The lossless convexification enables the use of interior point methods of convex optimization to obtain optimal solutions of the original nonconvex optimal control problem.