A major issue in Lagrangian relaxation for integer programming problems is to maximize the dual function which is piece-wise linear, and consists of many facets. Available methods include the subgradient method, the bundle method, and the recently developed surrogate subgradient method. Each of the above methods, however, has its own limitations. Based on the insights obtained from these method...

recently, gasimov and yenilmez proposed an approach for solving two kinds of fuzzy linear programming (flp) problems. through the approach, each flp problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. then, the crisp problem is solved by the use of the modified subgradient method. in this paper we will have another look at the earlier defuzzifi...

Recently, Gasimov and Yenilmez proposed an approach for solving two kinds of fuzzy linear programming (FLP) problems. Through the approach, each FLP problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. Then, the crisp problem is solved by the use of the modified subgradient method. In this paper we will have another look at the earlier defuzzifi...

Stochastic subgradient methods play an important role in machine learning. We introduced the concepts of subgradient methods and stochastic subgradient methods in this project, discussed their convergence conditions as well as the strong and weak points against their competitors. We demonstrated the application of (stochastic) subgradient methods to machine learning with a running example of tr...

In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...

This paper describes the Subgradient Marching algorithm to compute the derivative of the geodesic distance with respect to the metric. The geodesic distance being a concave function of the metric, this algorithm computes an element of the subgradient in O(N log(N)) operations on a discrete grid ofN points. It performs a front propagation that computes the subgradient of a discrete geodesic dist...

We extend the classic convergence rate theory for subgradient methods to apply to non-Lipschitz functions. For the deterministic projected subgradient method, we present a global O(1/ √ T ) convergence rate for any convex function which is locally Lipschitz around its minimizers. This approach is based on Shor’s classic subgradient analysis and implies generalizations of the standard convergenc...

In the networking research literature, the problem of network utility optimization is often converted to the dual problem which, due to nondifferentiability, is solved with a particular subgradient technique. This technique is not an ascent scheme, hence each iteration does not necessarily improve the value of the dual function. This paper examines the performance of this computational techniqu...

We present a unifying framework for nonsmooth convex minimization bringing together -subgradient algorithms and methods for the convex feasibility problem. This development is a natural step for -subgradient methods in the direction of constrained optimization since the Euclidean projection frequently required in such methods is replaced by an approximate projection, which is often easier to co...