Novel coordinate descent (CD) methods are proposed for minimizing nonconvex functions consisting of three terms: (i) a continuously differentiable term, (ii) simple convex and (iii) concave continuous term. First, by extending randomized CD to nonsmooth settings, we develop subgradient method that randomly updates block-coordinate variables using block composite mapping. This converges asymptot...

The feasibility problem for constant scaling in output feedback control is considered. This is an inherently di cult problem [20, 21] since the set of feasible solutions is nonconvex and may be disconnected. Nevertheless, we show that this problem can be reduced to the global maximization of a concave function over a convex set, or alternatively, to the global minimization of a convex program w...

The approximation of the convex envelope of nonconvex functions is an essential part in deterministic global optimization techniques (Floudas inDeterministic Global Optimization: Theory, Methods and Application, 2000). Current convex underestimation algorithms for multilinear terms, based on arithmetic intervals or recursive arithmetic intervals (Hamed in Calculation of bounds on variables and ...

This paper proposes an initialization approach for parameter estimation problems (PEPs) involving parameter-affine dynamic models. By using the state measurements, the nonconvex PEP is modified such that a convex approximation to the original PEP is obtained. The modified problem is solved by vailable online 5 November 2009 eywords: arameter estimation ultiple shooting onvex optimization convex...

In this paper, the multiple-input multiple-output (MIMO) transmit beampattern matching problem is considered. The problem is formulated to approximate a desired transmit beampattern (i.e., an energy distribution in space and frequency) and to minimize the cross-correlation of signals reflected back to the array by considering different practical waveform constraints at the same time. Due to the...

Classical multidimensional scaling constructs a configuration of points that minimizes a certain measure of discrepancy between the configuration’s interpoint distance matrix and a fixed dissimilarity matrix. Recent extensions have replaced the fixed dissimilarity matrix with a closed and convex set of dissimilarity matrices. These extensions lead to optimization problems with two sets of decis...

The popular cubic regularization (CR) method converges with firstand second-order optimality guarantee for nonconvex optimization, but encounters a high sample complexity issue for solving large-scale problems. Various sub-sampling variants of CR have been proposed to improve the sample complexity. In this paper, we propose a stochastic variance-reduced cubic-regularized (SVRC) Newton’s method ...