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.

Synthesis of Sparse Arrays With Focused or Shaped Beampattern via Sequential Convex Optimizations

Abstract: An iterative procedure for the synthesis of sparse arrays radiating focused or shaped beampattern is presented The algorithm consists in solving a sequence of weighted l1 convex optimization problems The method can thus be readily implemented and efficiently solved In the optimization procedure, the objective is the minimization of the number of radiating elements and the constraints correspond to the pattern requirements The method can be applied to synthesize either focused or shaped beampattern and there is no restriction regarding the array geometry and individual element patterns Numerical comparisons with standard benchmark problems assess the efficiency of the proposed approach, whose computation time is several orders of magnitude below those of so-called global optimization algorithms

The Bounded Real Lemma for Internally Positive Systems and H-Infinity Structured Static State Feedback

Abstract: We consider the bounded real lemma for internally positive linear time-invariant systems. We show that the H∞ norm of such systems can be evaluated by checking the existence of a certain diagonal quadratic storage function. Taking advantage of this fact, the problem of designing a structured static state feedback controller achieving internal stability, contractiveness, and internal positivity in closed loop becomes convex and tractable.

Interference-Limited Resource Optimization in Cognitive Femtocells With Fairness and Imperfect Spectrum Sensing

Abstract: The use of cognitive-radio(CR)-enabled femtocell is regarded as a promising technique in wireless communications, and many studies have been reported on its resource allocation and interference management. However, fairness and spectrum sensing errors were ignored in most of the existing studies. In this paper, we propose a resource allocation scheme for orthogonal frequency division multiple access (OFDMA)-based cognitive femtocells. The target is to maximize the total capacity of all femtocell users (FUs) under given quality-of-service (QoS) and cotier/cross-tier interference constraints with imperfect channel sensing. To achieve the fairness among FUs, the minimum and maximum numbers of subchannels occupied by each user are considered. First, the subchannel and power allocation problem is modeled as a mixed-integer programming problem, and then, it is transformed into a convex optimization problem by relaxing subchannel sharing and applying cotier interference constraints, which is finally solved using a dual decomposition method. Based on the obtained solution, an iterative subchannel and power allocation algorithm is proposed. The effectiveness of the proposed algorithm in terms of capacity and fairness compared with the existing schemes is verified by simulations.

A Note on the Alternating Direction Method of Multipliers

Abstract: We consider the linearly constrained separable convex programming, whose objective function is separable into m individual convex functions without coupled variables. The alternating direction method of multipliers has been well studied in the literature for the special case m=2, while it remains open whether its convergence can be extended to the general case m≥3. This note shows the global convergence of this extension when the involved functions are further assumed to be strongly convex.

Trace Norm Regularization: Reformulations, Algorithms, and Multi-Task Learning

Abstract: We consider a recently proposed optimization formulation of multi-task learning based on trace norm regularized least squares. While this problem may be formulated as a semidefinite program (SDP), its size is beyond general SDP solvers. Previous solution approaches apply proximal gradient methods to solve the primal problem. We derive new primal and dual reformulations of this problem, including a reduced dual formulation that involves minimizing a convex quadratic function over an operator-norm ball in matrix space. This reduced dual problem may be solved by gradient-projection methods, with each projection involving a singular value decomposition. The dual approach is compared with existing approaches and its practical effectiveness is illustrated on simulations and an application to gene expression pattern analysis.