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.

Robust Adaptive Beamforming Using Sequential Quadratic Programming: An Iterative Solution to the Mismatch Problem

Abstract: A new approach to the design of robust adaptive beamforming is introduced. The essence of the new approach is to estimate the difference between the actual and presumed steering vectors and to use this difference to correct the erroneous presumed steering vector. The estimation process is performed iteratively where a quadratic convex optimization problem is solved at each iteration. Contrary to the worst-case performance-based and the probability-constrained-based approaches, our approach does not make any assumptions on either the norm of the mismatch vector or its probability distribution. Hence, it avoids the need for estimating their values.

Digital Circuit Optimization via Geometric Programming

Abstract: This paper concerns a method for digital circuit optimization based on formulating the problem as a geometric program (GP) or generalized geometric program (GGP), which can be transformed to a convex optimization problem and then very efficiently solved. We start with a basic gate scaling problem, with delay modeled as a simple resistor-capacitor (RC) time constant, and then add various layers of complexity and modeling accuracy, such as accounting for differing signal fall and rise times, and the effects of signal transition times. We then consider more complex formulations such as robust design over corners, multimode design, statistical design, and problems in which threshold and power supply voltage are also variables to be chosen. Finally, we look at the detailed design of gates and interconnect wires, again using a formulation that is compatible with GP or GGP.

Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach

Abstract: When there is parameter uncertainty in the constraints of a convex optimization problem, it is natural to formulate the problem as a joint chance constrained program (JCCP), which requires that all constraints be satisfied simultaneously with a given large probability. In this paper, we propose to solve the JCCP by a sequence of convex approximations. We show that the solutions of the sequence of approximations converge to a Karush-Kuhn-Tucker (KKT) point of the JCCP under a certain asymptotic regime. Furthermore, we propose to use a gradient-based Monte Carlo method to solve the sequence of convex approximations.

Optimization by decomposition and coordination: A unified approach

Abstract: In the general framework of inifinite-dimensional convex programming, two fundamental principles are demonstrated and used to derive several basic algorithms to solve a so-called "master" (constrained optimization) problem. These algorithms consist in solving an infinite sequence of "auxiliary" problems whose solutions converge to the master's optimal one. By making particular choices for the auxiliary problems, one can recover either classical algorithms (gradient, Newton-Raphson, Uzawa) or decomposition-coordination (two-level) algorithms. The advantages of the theory are that it clearly sets the connection between classical and two-level algorithms, It provides a framework for classifying the two-level algorithms, and it gives a systematic way of deriving new algorithms.