In this paper, we propose a framework of Inexact Proximal Stochastic Second-order (IPSS) methods for solving nonconvex optimization problems, whose objective function consists of an average of finitely many, possibly weakly, smooth functions and a convex but possibly nons- mooth function. At each iteration, IPSS inexactly solves a proximal subproblem constructed by using some positive … Read more
This work presents the results of experimental operation of a solar-driven climate system using mixed-integer nonlinear Model Predictive Control (MPC). The system is installed in a university building and consists of two solar thermal collector fields, an adsorption cooling machine with different operation modes, a stratified hot water storage with multiple inlets and outlets as … Read more
This report gives a concise overview into genericity results for sets of matrices, linear and nonlinear equations as well as for unconstrained and constrained optimization problems. We present the generic behavior of non-parametric problems and parametric families of problems. The genericity analysis is based on results from differential geometry, in particular transversality theorems. Article Download … Read more
This paper considers linear quadratic optimal control problem of large-scale interconnected systems. An algorithmic framework is constructed to design controllers that provide a desired tradeoff between the system performance and the sparsity of the static feedback matrix. This is accomplished by introducing a minimization problem involving $\ell_0-$norm of the feedback matrix subject to a maximum … Read more
We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (SIAM J. Matrix Anal. Appl., 28(1), 2006) describe how to apply the conjugate gradient (CG) method coupled with a constraint preconditioner, a choice that has proved to be … Read more
Cubic Regularization methods have several favorable properties. In particular under mild assumptions, they are globally convergent towards critical points with second order necessary conditions satisfied. Their adoption among practitioners, however, does not yet match the strong theoretical results. One of the reasons for this discrepancy may be additional implementation complexity needed to solve the occurring … Read more
We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic 1d partial differential equations. In addition, a pooling-type mixing model is required at the nodes of the network to treat the mixing … Read more
A popular belief for explaining the efficiency in training deep neural networks is that over-paramenterized neural networks have nice landscape. However, it still remains unclear whether over-parameterized neural networks contain spurious local minima in general, since all current positive results cannot prove non-existence of bad local minima, and all current negative results have strong restrictions … Read more
We present a stochastic extension of the mesh adaptive direct search (MADS) algorithm originally developed for deterministic blackbox optimization. The algorithm, called StoMADS, considers the unconstrained optimization of an objective function f whose values can be computed only through a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based … Read more
We consider optimization of differential-algebraic equations (DAEs) with complementarity constraints (CCs) of algebraic state pairs. Formulating the CCs as smoothed nonlinear complementarity problem (NCP) functions leads to a smooth DAE, allowing for the solution in direct shooting. We provide sufficient conditions for well-posedness. Thus, we can prove that with the smoothing parameter going to zero, … Read more