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 published on a yearly basis
Papers
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TL;DR: The most frequently used ways of dealing with parameter uncertainties, including polytopic and norm-bounded characterizations, have been taken into consideration, with convex optimization problems obtained for the design of desired robust energy-to-peak filters.
288 citations
Proceedings Article•
12 Dec 2011TL;DR: A novel analysis is provided, which shows how standard gradient methods may sometimes be insufficient to obtain a significant speed-up and a novel accelerated gradient algorithm is proposed, which deals with this deficiency, enjoys a uniformly superior guarantee and works well in practice.
Abstract: Mini-batch algorithms have been proposed as a way to speed-up stochastic convex optimization problems. We study how such algorithms can be improved using accelerated gradient methods. We provide a novel analysis, which shows how standard gradient methods may sometimes be insufficient to obtain a significant speed-up and propose a novel accelerated gradient algorithm, which deals with this deficiency, enjoys a uniformly superior guarantee and works well in practice.
287 citations
13 Jun 2001
TL;DR: This work considers the general nonlinear optimization problem in 0- 1 variables and provides an explicit equivalent convex positive semidefinite program in 2n - 1 variables that is equivalent to the optimal values of both problems.
Abstract: We consider the general nonlinear optimization problem in 0- 1 variables and provide an explicit equivalent convex positive semidefinite program in 2n - 1 variables. The optimal values of both problems are identical. From every optimal solution of the former one easily find an optimal solution of the latter and conversely, from every solution of the latter one may construct an optimal solution of the former.
287 citations
01 Jan 1985
TL;DR: In this paper, the main known results about suuch functions from the viewpoint of analysis and optimization are surveyed, and a survey of the main features of these functions can be found.
Abstract: A function is called d. c. if it can be. expressed as a difference of two convex functions. In the present paper we survey the main known results about suuch functions from the viewpoint of Analysis and Optimization.
287 citations
TL;DR: A generalized iterative backward waterfilling algorithm is developed and based on the sequence of maximum departure regions at energy arrival instants, the transmission completion time minimization problem is decompose into convex optimization problems and solved efficiently.
Abstract: In this paper, we investigate the optimal packet scheduling problem in a two-user multiple access communication system, where the transmitters are able to harvest energy from the nature. Under a deterministic system setting, we assume that the energy harvesting times and harvested energy amounts are known before the transmission starts. For the packet arrivals, we assume that packets have already arrived and are ready to be transmitted at the transmitter before the transmission starts. Our goal is to minimize the time by which all packets from both users are delivered to the destination through controlling the transmission powers and transmission rates of both users. We first develop a generalized iterative backward waterfilling algorithm to characterize the maximum departure region of the transmitters for any given deadline T. Then, based on the sequence of maximum departure regions at energy arrival instants, we decompose the transmission completion time minimization problem into convex optimization problems and solve the overall problem efficiently.
286 citations