Logarithmic-Barrier Decomposition Interior-Point Methods for Stochastic Linear Optimization in a Hilbert Space

Several logarithmic-barrier interior-point methods are now available for solving two-stage stochastic optimization problems with recourse in the finite-dimensional setting. However, despite the genuine need for studying such methods in general spaces, there are no infinite-dimensional analogs of these methods. Inspired by this evident gap in the literature, in this paper, we propose logarithmic-barrier decomposition-based interior-point … Read more

Volumetric barrier decomposition algorithms for two-stage stochastic linear semi-infinite programming

In this paper, we study the two-stage stochastic linear semi-infinite programming with recourse to handle uncertainty in data defining (deterministic) linear semi-infinite programming. We develop and analyze volumetric barrier decomposition-based interior point methods for solving this class of optimization problems, and present a complexity analysis of the proposed algorithms. We establish our convergence analysis by … Read more

A logarithmic barrier interior-point method based on majorant functions for second-order cone programming

We present a logarithmic barrier interior-point method for solving a second-order cone programming problem. Newton’s method is used to compute the descent direction, and majorant functions are used as an efficient alternative to line search methods to determine the displacement step along the direction. The efficiency of our method is shown by presenting numerical experiments. … Read more

A primal-dual interior-point method based on various selections of displacement step for second-order cone programming

In this paper, a primal-dual interior-point method equipped with various selections of the displacement step are derived for solving second-order cone programming problems. We first establish the existence and uniqueness of the optimal solution of the corresponding perturbed problem and then demonstrate its convergence to the optimal solution of the original problem. Next, we present … Read more

The Jordan Algebraic Structure of the Circular Cone

In this paper, we study and analyze the algebraic structure of the circular cone. We establish a new efficient spectral decomposition, set up the Jordan algebra associated with the circular cone, and prove that this algebra forms a Euclidean Jordan algebra with a certain inner product. We then show that the cone of squares of … Read more

Extension and Implementation of Homogeneous Self-dual Methods for Symmetric Cones under Uncertainty

Homogeneous self-dual algorithms for stochastic semidefinite programs with finite event space has been proposed by Jin et al. in [12]. Alzalg [8], has adopted their work to derive homogeneous self-dual algorithms for stochastic second-order programs with finite event space. In this paper, we generalize these two results to derive homogeneous self-dual algorithms for stochastic programs … Read more