Browsing by Author "Kasap, S"

Now showing 1 - 2 of 2

Citation - WoS: 0
Differential Algebraic Equations in Primal Dual Interior Point Optimization Methods
(Amer inst Physics, 2004) Kasap, S; Kasap, Suat; Trafalis, TB; Endüstri Mühendisliği
Primal dual Interior Point Methods (IPMs) generate points that lie in the neighborhood of the central trajectory. The key ingredient of the primal dual IPMs is the parameterization of the central trajectory. A new approach to the parameterization of the central trajectory is presented. Instead of parameterizing the central trajectory by the barrier parameter, it is parameterized by the time by describing a continuous dynamical system. Specifically, a new update rule based on the solution of an ordinary differential equation for the barrier parameter of the primal dual IPMs is presented. The resulting ordinary differential equation combined with the first order Karush-Kuhn-Tucker (KKT) conditions, which are algebraic equations, are called differential algebraic equations (DAEs). By solving DAEs, we find an optimal solution to the given problem.
Citation - WoS: 0
An Overview of Mean Field Theory in Combinatorial Optimization Problems
(Amer inst Physics, 2004) Kasap, S; Trafalis, TB
In the last three decades, there has been significant interest in using mean field theory of statistical physics for combinatorial optimization. This has led to the development of powerful optimization techniques such as neural networks (NNs), simulated annealing (SA), and mean field annealing (MFA). MFA replaces the stochastic nature of SA with a set of deterministic equations named as mean field equations. The mean field equations depend on the energy function of the NNs and are solved at each temperature during the annealing process of SA. MFA advances to the optimal solution in a fundamentally different way than stochastic methods. The use of mean field techniques for the combinatorial optimization problems are reviewed in this study.