The characterization and numerical solution of two non-smooth optimal control problems governed by a Fokker–Planck (FP) equation are investigated in the framework of the Pontryagin maximum principle (PMP). The two FP control problems are related to the problem of determining open- and...

In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the...

<Para ID="Par1">Clustering is an important problem in data mining. It can be formulated as a nonsmooth, nonconvex optimization problem. For the most global optimization techniques this problem is challenging even in medium size data sets. In this paper, we propose an approach that allows one to apply local...</para>

<Para ID="Par1">Differential evolution (DE) is a new population-based stochastic optimization, which has difficulties in solving large-scale and multimodal optimization problems. The reason is that the population diversity decreases rapidly, which leads to the failure of the clustered individuals to reproduce...</para>

Penalty function methods are popular in dealing with the constrained optimization problems. How to choose reasonable penalty coefficients is a crucial problem which usually poses great influence on the quality of the final solution found. In this paper, the definition of the minimum penalty...

We present a primal-dual active-set framework for solving large-scale convex quadratic optimization problems (QPs). In contrast to classical active-set methods, our framework allows for multiple simultaneous changes in the active-set estimate, which often leads to rapid identification of the...

<Para ID="Par1">Locating a semi-obnoxious facility, like an airport or correctional center is typically a bi-criterion problem combining a convex objective function representing minimum transportation cost with a multi-extremal objective function representing the non-desirable part of the facility. Generic one...</para>

<Para ID="Par1">In this paper, we consider an inverse problem of identifying one or more unknown cavities in a heat conductor. We propose an algorithm for reconstructing the position and shape of the unknown cavities using the measured surface temperature of the heat conductor. The heat conductor is discretized...</para>

This paper is aimed to employ a modified quasi-Newton equation in the framework of the limited memory BFGS method to solve large-scale unconstrained optimization problems. The modified secant equation is derived by means of a forth order tensor model to improve the curvature information of the...