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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
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Journal ArticleDOI
TL;DR: The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities and the relation to frequency domain methods such as the circle and Popov criteria is explained.
Abstract: This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods such as the circle and Popov criteria is explained. Several examples are included to demonstrate the flexibility and power of the approach.

1,186 citations

Journal ArticleDOI
TL;DR: The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative as mentioned in this paper.
Abstract: The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function. We also provide conditions for the value function to be, variously, absolutely continuous, left- and right-differentiable, or fully differentiable. These results are applied to mechanism design, convex programming, continuous optimization problems, saddle-point problems, problems with parameterized constraints, and optimal stopping problems.

1,183 citations

Journal ArticleDOI
TL;DR: It is shown that the MDA can be viewed as a nonlinear projected-subgradient type method, derived from using a general distance-like function instead of the usual Euclidean squared distance, and derived in a simple way convergence and efficiency estimates.

1,183 citations

Journal ArticleDOI
TL;DR: The problem of finding the (symmetric) edge weights that result in the least mean-square deviation in steady state is considered and it is shown that this problem can be cast as a convex optimization problem, so the global solution can be found efficiently.

1,166 citations

Journal ArticleDOI
TL;DR: In this article, the authors developed a mathematical theory of super-resolution, which is the problem of recovering the details of an object from coarse scale information only from samples at the low end of the spectrum.
Abstract: This paper develops a mathematical theory of super-resolution. Broadly speaking, superresolution is the problem of recovering the ne details of an object|the high end of its spectrum| from coarse scale information only|from samples at the low end of the spectrum. Suppose we have many point sources at unknown locations in [0; 1] and with unknown complex-valued amplitudes. We only observe Fourier samples of this object up until a frequency cut-o fc. We show that one can super-resolve these point sources with innite precision|i.e. recover the exact locations and amplitudes|by solving a simple convex optimization problem, which can essentially be reformulated as a semidenite program. This holds provided that the distance between sources is at least 2=fc. This result extends to higher dimensions and other models. In one dimension for instance, it is possible to recover a piecewise smooth function by resolving the discontinuity points with innite precision as well. We also show that the theory and methods are robust to noise. In particular, in the discrete setting we develop some theoretical results explaining how the accuracy of the super-resolved signal is expected to degrade when both the noise level and the super-resolution factor vary.

1,157 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023392
2022849
20211,461
20201,673
20191,677
20181,580