1,050 research outputs found
Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints
This paper investigates the relation between sequential convex programming
(SCP) as, e.g., defined in [24] and DC (difference of two convex functions)
programming. We first present an SCP algorithm for solving nonlinear
optimization problems with DC constraints and prove its convergence. Then we
combine the proposed algorithm with a relaxation technique to handle
inconsistent linearizations. Numerical tests are performed to investigate the
behaviour of the class of algorithms.Comment: 18 pages, 1 figur
An Inequality Constrained SL/QP Method for Minimizing the Spectral Abscissa
We consider a problem in eigenvalue optimization, in particular finding a
local minimizer of the spectral abscissa - the value of a parameter that
results in the smallest value of the largest real part of the spectrum of a
matrix system. This is an important problem for the stabilization of control
systems. Many systems require the spectra to lie in the left half plane in
order for them to be stable. The optimization problem, however, is difficult to
solve because the underlying objective function is nonconvex, nonsmooth, and
non-Lipschitz. In addition, local minima tend to correspond to points of
non-differentiability and locally non-Lipschitz behavior. We present a
sequential linear and quadratic programming algorithm that solves a series of
linear or quadratic subproblems formed by linearizing the surfaces
corresponding to the largest eigenvalues. We present numerical results
comparing the algorithms to the state of the art
A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming
This work presents the concept of kernel mean embedding and kernel
probabilistic programming in the context of stochastic systems. We propose
formulations to represent, compare, and propagate uncertainties for fairly
general stochastic dynamics in a distribution-free manner. The new tools enjoy
sound theory rooted in functional analysis and wide applicability as
demonstrated in distinct numerical examples. The implication of this new
concept is a new mode of thinking about the statistical nature of uncertainty
in dynamical systems
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