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In this work, we give a tight estimate of the rate of convergence for the Halpern-iteration for approximating a fixed point of a nonexpansive mapping in a Hilbert space. Specifically, using semidefinite programming and duality we prove that the norm of the residuals is upper bounded by the...

This paper develops a distributionally robust joint chance constrained optimization model for a dynamic network design problem (NDP) under demand uncertainty. The major contribution of this paper is to propose an approach to approximate a joint chance-constrained Cell Transmission Model (CTM)...

This paper is concerned with the Multi-Row Facility Layout Problem. Given a set of rectangular departments, a fixed number of rows, and weights for each pair of departments, the problem consists of finding an assignment of departments to rows and the positions of the departments in each row so...

In this paper we present the algorithmic framework and practical aspects of implementing a parallel version of a primal-dual semidefinite programming solver on a distributed memory computer cluster. Our implementation is based on the CSDP solver and uses a message passing interface (MPI), and...

We address the multi-period portfolio optimization problem with the constant rebalancing strategy. This problem is formulated as a polynomial optimization problem (POP) by using a mean-variance criterion. In order to solve the POPs of high degree, we develop a cutting-plane algorithm based on...

In this paper, we propose a second-order corrector interior-point algorithm for semidefinite programming (SDP). This algorithm is based on the wide neighborhood. The complexity bound is $${O(\sqrt{n}L)}$$ for the Nesterov-Todd direction, which coincides with the best known complexity results for...

We present an inexact spectral bundle method for solving convex quadratic semidefinite optimization problems. This method is a first-order method, hence requires much less computational cost in each iteration than second-order approaches such as interior-point methods. In each iteration of our...

Based on a novel reformulation of the feasible region, we propose and analyze a partial Lagrangian relaxation approach for the unbalanced orthogonal Procrustes problem (UOP). With a properly selected Lagrangian multiplier, the Lagrangian relaxation (LR) is equivalent to the recent matrix lifting...