We develop an active set method for solving second-order cone programs that may have an arbitrary number of linear constraints but are restricted to have only one second-order cone constraint. Problems of this form arise in the context of robust optimization and trust region methods. The proposed active set method exploits the fact that a second-order cone program with only one second-order con...

We transform a 2-dimensional second-order cone program to a standard linear program in order to pivot a vector based on its three states. Related properties of the transformation are given. Based on the transformation, we interpret the simplex method and its sensitivity analysis for the 2-dimensional second-order cone programming, especially the state changes. Finally, we give some applications...

a method has been presented for finding the solution surface of the npde: u  c , bounded by a general space curve. the method is based on the geometric characteristics of the surface, and is called the “cone-slot method”. it has been shown that such a surface can be obtained by movement of a cone inside the slot formed by the boundary space curve. an algorithm has been suggested on the basis ...

Wind turbines and associated parts are susceptible to cyclic stresses, including torque, bending, longitudinal stress, twisting moments. Therefore, research on the resilience of dynamic systems under such high loads is crucial for design future risk‐free operations. The method described in this study beneficial multidimensional structural responses that have undergone sufficient numerical simul...

The Q method of semidefinite programming, developed by Alizadeh, Haeberly and Overton, is extended to optimization problems over symmetric cones. At each iteration of the Q method, eigenvalues and Jordan frames of decision variables are updated using Newton’s method. We give an interior point and a pure Newton’s method based on the Q method. In another paper, the authors have shown that the Q m...

This paper contains the following results for ecohomies with infinite dimensional commodity spaces. (i) We establish a core-Walras equivalence theorem for economies with an atomless measure space of agents and with an ordered separable Banach commodity space whose positive cone has a non-empty norm interior. This result includes as a special case the Aumann (1964) and Schmeidler-Hildenbrand [Hi...