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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
Mario A. Rotea1
TL;DR: Keywords .

219 citations

Book
23 Dec 2011
TL;DR: Optimization with Sparsity-Inducing Penalties presents optimization tools and techniques dedicated to such sparsity-inducing penalties from a general perspective and provides an extensive set of experiments to compare various algorithms from a computational point of view.
Abstract: Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate nonsmooth norms. Optimization with Sparsity-Inducing Penalties presents optimization tools and techniques dedicated to such sparsity-inducing penalties from a general perspective. It covers proximal methods, block-coordinate descent, reweighted 2-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provides an extensive set of experiments to compare various algorithms from a computational point of view. The presentation of Optimization with Sparsity-Inducing Penalties is essentially based on existing literature, but the process of constructing a general framework leads naturally to new results, connections and points of view. It is an ideal reference on the topic for anyone working in machine learning and related areas.

218 citations

Journal ArticleDOI
TL;DR: The proposed branch and bound type algorithm attains finite ϵ-convergence to the global minimum through the successive refinement of a convex relaxation of the feasible region and/or of the objective function and the subsequent solution of a series of nonlinear convex optimization problems.

218 citations

Journal ArticleDOI
TL;DR: Convex and semidefinite optimization methods, duality, and complexity theory are introduced to shed new light on the relation of option and stock prices based just on the no-arbitrage assumption, and it is shown that it is NP-hard to find best possible bounds in multiple dimensions.
Abstract: The idea of investigating the relation of option and stock prices based just on the no-arbitrage assumption, but without assuming any model for the underlying price dynamics, has a long history in the financial economics literature. We introduce convex and, in particular semidefinite optimization methods, duality, and complexity theory to shed new light on this relation. For the single stock problem, given moments of the prices of the underlying assets, we show that we can find best-possible bounds on option prices with general payoff functions efficiently, either algorithmically (solving a semidefinite optimization problem) or in closed form. Conversely, given observable option prices, we provide best-possible bounds on moments of the prices of the underlying assets, as well as on the prices of other options on the same asset by solving linear optimization problems. For options that are affected by multiple stocks either directly (the payoff of the option depends on multiple stocks) or indirectly (we have information on correlations between stock prices), we find nonoptimal bounds using convex optimization methods. However, we show that it is NP-hard to find best possible bounds in multiple dimensions. We extend our results to incorporate transactions costs.

218 citations

Journal ArticleDOI
TL;DR: A criterion is derived to ensure the exponential stability of the error dynamics, which fully utilizes the available information about the actual sampling pattern, and the design method of the desired sampled-data controllers is proposed to make the CDNs exponentially synchronized and obtain a lower-bound estimation of the largest sampling interval.
Abstract: This paper studies the problem of sampled-data exponential synchronization of complex dynamical networks (CDNs) with time-varying coupling delay and uncertain sampling. By combining the time-dependent Lyapunov functional approach and convex combination technique, a criterion is derived to ensure the exponential stability of the error dynamics, which fully utilizes the available information about the actual sampling pattern. Based on the derived condition, the design method of the desired sampled-data controllers is proposed to make the CDNs exponentially synchronized and obtain a lower-bound estimation of the largest sampling interval. Simulation examples demonstrate that the presented method can significantly reduce the conservatism of the existing results, and lead to wider applications.

218 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