scispace - formally typeset
Search or ask a question
Topic

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.


Papers
More filters
Journal ArticleDOI
TL;DR: This paper represents an attempt to apply second-order cone programming, a branch of convex optimization, to the class of highly nonlinear trajectory optimization problems in entry flight with a combination of successive linearization and relaxation techniques.
Abstract: Convex optimization has found wide applications in recent years due to its unique theoretical advantages and the polynomial-time complexity of state-of-the-art solution algorithms for convex programming This paper represents an attempt to apply second-order cone programming, a branch of convex optimization, to the class of highly nonlinear trajectory optimization problems in entry flight The foremost challenge in applying convex optimization in most aerospace engineering problems lies in the nonlinearity and nonconvexity of the problem Exclusive reliance on linearization does not always work well, as is the case in entry trajectory optimization This paper focuses on how to formulate realistic, highly constrained entry trajectory optimization problems in a fashion suitable to be solved by second-order cone programming with a combination of successive linearization and relaxation techniques Rigorous analysis is conducted to support the soundness of the approach Numerical demonstrations are provided to

210 citations

Journal ArticleDOI
TL;DR: The results show that the proposed sub-optimal solution achieves close-to-bound sum-rate performance, which is significantly better than that of time-division multiple access.
Abstract: In this paper, we explore non-orthogonal multiple access (NOMA) in millimeter-wave (mm-wave) communications (mm-wave-NOMA). In particular, we consider a typical problem, i.e., maximization of the sum rate of a 2-user mm-wave-NOMA system. In this problem, we need to find the beamforming vector to steer towards the two users simultaneously subject to an analog beamforming structure, while allocating appropriate power to them. As the problem is non-convex and may not be converted to a convex problem with simple manipulations, we propose a suboptimal solution to this problem. The basic idea is to decompose the original joint beamforming and power allocation problem into two sub-problems which are relatively easy to solve: one is a power and beam gain allocation problem, and the other is a beamforming problem under a constant-modulus constraint. Extension of the proposed solution from 2-user mm-wave-NOMA to more-user mm-wave-NOMA is also discussed. Extensive performance evaluations are conducted to verify the rational of the proposed solution, and the results also show that the proposed sub-optimal solution achieves close-to-bound sum-rate performance, which is significantly better than that of time-division multiple access.

209 citations

Journal ArticleDOI
TL;DR: A novel method for exactly reformulating nondifferentiable collision avoidance constraints into smooth, differentiable constraints using strong duality of convex optimization on a controlled object whose goal is to avoid obstacles while moving in an $n$ -dimensional space is presented.
Abstract: This article presents a novel method for exactly reformulating nondifferentiable collision avoidance constraints into smooth, differentiable constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid obstacles while moving in an $n$ -dimensional space. The proposed reformulation is exact, does not introduce any approximations, and applies to general obstacles and controlled objects that can be represented as the union of convex sets. We connect our results with the notion of signed distance, which is widely used in traditional trajectory generation algorithms. Our method can be applied to generic navigation and trajectory planning tasks, and the smoothness property allows the use of general-purpose gradient- and Hessian-based optimization algorithms. Finally, in case a collision cannot be avoided, our framework allows us to find “least-intrusive” trajectories, measured in terms of penetration. We demonstrate the efficacy of our framework on an automated parking problem, where our numerical experiments suggest that the proposed method is robust and enables real-time optimization-based trajectory planning in tight environments. Sample code of our example is provided at https://github.com/XiaojingGeorgeZhang/OBCA .

209 citations

Journal ArticleDOI
TL;DR: In this paper, robust global stability analysis for generalized neural networks (GNNs) with both discrete and distributed delays is addressed. But the authors assume that the parameter uncertainties are time invariant and bounded, and belong to given compact sets.
Abstract: This paper is concerned with the problem of robust global stability analysis for generalized neural networks (GNNs) with both discrete and distributed delays. The parameter uncertainties are assumed to be time-invariant and bounded, and belong to given compact sets. The existence of the equilibrium point is first proved under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, by employing a Lyapunov–Krasovskii functional, the addressed stability analysis problem is converted into a convex optimization problem, and a linear matrix inequality (LMI) approach is utilized to establish the sufficient conditions for the globally robust stability for the GNNs, with and without parameter uncertainties. These conditions can be readily checked by utilizing the Matlab LMI toolbox. A numerical example is provided to demonstrate the usefulness of the proposed global stability condition.

209 citations

Journal ArticleDOI
TL;DR: In this article, a primal-dual fixed point algorithm based on the proximity operator (PDFP2Oκ for κ ∈ [0, 1)) was proposed and obtained a closed-form solution for each iteration.
Abstract: Recently, the minimization of a sum of two convex functions has received considerable interest in a variational image restoration model. In this paper, we propose a general algorithmic framework for solving a separable convex minimization problem from the point of view of fixed point algorithms based on proximity operators (Moreau 1962 C. R. Acad. Sci., Paris I 255 2897–99). Motivated by proximal forward–backward splitting proposed in Combettes and Wajs (2005 Multiscale Model. Simul. 4 1168–200) and fixed point algorithms based on the proximity operator (FP2O) for image denoising (Micchelli et al 2011 Inverse Problems 27 45009–38), we design a primal–dual fixed point algorithm based on the proximity operator (PDFP2Oκ for κ ∈ [0, 1)) and obtain a scheme with a closed-form solution for each iteration. Using the firmly nonexpansive properties of the proximity operator and with the help of a special norm over a product space, we achieve the convergence of the proposed PDFP2Oκ algorithm. Moreover, under some stronger assumptions, we can prove the global linear convergence of the proposed algorithm. We also give the connection of the proposed algorithm with other existing first-order methods. Finally, we illustrate the efficiency of PDFP2Oκ through some numerical examples on image supper-resolution, computerized tomographic reconstruction and parallel magnetic resonance imaging. Generally speaking, our method PDFP2O (κ = 0) is comparable with other state-of-the-art methods in numerical performance, while it has some advantages on parameter selection in real applications.

209 citations


Network Information
Related Topics (5)
Optimization problem
96.4K papers, 2.1M citations
94% related
Robustness (computer science)
94.7K papers, 1.6M citations
89% related
Linear system
59.5K papers, 1.4M citations
88% related
Markov chain
51.9K papers, 1.3M citations
86% related
Control theory
299.6K papers, 3.1M citations
83% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023392
2022849
20211,461
20201,673
20191,677
20181,580