joint work with Refail Kasimbeyli
In this study, we present a version of the Cutting-Plane Method, developed for minimizing a nonconvex function. We use weak subgradients which is based on the idea of supporting conic surfaces. This supporting approach does not require convexity condition on the function. The suggested method, minimizes the pointwise maximum of superlinear functions, by the weak subgradient. Since the graphs of supporting functions are conical surfaces, the new method is called the "Cutting Conic Surfaces Method". The subproblem is “linearized” and some illustrative examples are provided. Acknowledgment : This study is supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under the Grant No. 217M487.
joint work with Antonio Frangioni
The aim of the open-source Structured Modeling System++ (SMS++) is to facilitate the implementation of general and flexible algorithms for optimization problems with several nested layers of structure. We will present the current state of SMS++, focussing on recent developments concerning the representation of uncertainty, which are meant to facilitate the transformation of complex deterministic models into stochastic ones. Specific SMS++ facilities for "general-purpose decomposition techniques" will then allow to efficiently produce multi-level decomposition approaches to these problems.
joint work with Gulcin Dinc Yalcin
This work presents a weak subgradient based solution method in nonconvex unconstrained optimization. The weak subgradient notion does not require convexity condition on the function under consideration, and hence allows to investigate a wide class of nonconvex optimization problems. By using relationships between the weak subgradients and the radial epiderivatives, we present a method for approximate estimation of weak subgradients, and use it to update a current solution. The convergence theorems for the presented method, are established and the illustrative examples are provided. Acknowledgment : This study is supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under the Grant No. 217M487.