abstract: in this thesis, we focus to class of convex optimization problem whose objective function is given as a linear function and a convex function of a linear transformation of the decision variables and whose feasible region is a polytope. we show that there exists an optimal solution to this class of problems on a face of the constraint polytope of feasible region. based on this, we dev...

In this study, the temperature in friction stir welding of duplex stainless steel has been investigated. At first, temperature estimation was modeled and estimated at different distances from the center of the stir zone by the multivariate Lagrangian function. Then, the linear extrapolation method and multiple linear regression method were used to estimate the temperature outside the range and ...