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: A convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed-loop uncertain system.
372 citations
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TL;DR: This work uses time-domain input-output data to validate uncertainty models and develops algorithms that are computationally tractable and reduce to (generally nondifferentiable) convex feasibility problems or to linear programming problems.
Abstract: In this paper we offer a novel approach to control-oriented model validation problems. The problem is to decide whether a postulated nominal model with bounded uncertainty is consistent with measured input-output data. Our approach directly uses time-domain input-output data to validate uncertainty models. The algorithms we develop are computationally tractable and reduce to (generally nondifferentiable) convex feasibility problems or to linear programming problems. In special cases, we give analytical solutions to these problems. >
372 citations
01 Jan 2011
372 citations
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16 Dec 1998TL;DR: In this article, linear matrix inequalities (LMI) are used to perform local stability and performance analysis of linear systems with saturating elements, which leads to less conservative information on stability regions, disturbance rejection, and L/sub 2/gain than standard global stability analysis.
Abstract: We show how linear matrix inequalities (LMI) can be used to perform local stability and performance analysis of linear systems with saturating elements. This leads to less conservative information on stability regions, disturbance rejection, and L/sub 2/-gain than standard global stability and performance analysis. The circle and Popov criteria are used to obtain Lyapunov functions whose sublevel sets provide regions of guaranteed stability and performance within a restricted state space region. Our LMI formulation leads directly to simple convex optimization problems that can be solved efficiently as semidefinite programs. The results cover both single and multiple saturation elements and can be immediately extended to discrete time systems. An obvious application of these techniques is in the analysis of control systems with saturating control inputs.
372 citations
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IBM1
TL;DR: In this paper, an algorithm for finding the minimum of any convex, not necessarily differentiable, function f of several variables is described, which yields a sequence of points tending to the solution of the problem, if any, requiring only the calculation of f and one subgradient of f at designated points.
Abstract: An algorithm is described for finding the minimum of any convex, not necessarily differentiable, function f of several variables. The algorithm yields a sequence of points tending to the solution of the problem, if any, requiring only the calculation of f and one subgradient of f at designated points. Its rate of convergence is estimated for convex and for differentiable convex functions. For the latter, it is an extension of the method of conjugate gradients and terminates for quadratic functions.
371 citations