We show that the problem of computing sharp upper and lower static-arbitrage bounds on the price of a European basket option, given the prices of other similar options, can be cast as a linear program (LP). The LP formulations readily yield super-replicating (sub-replicating) strategies for the upper (lower) bound problem. The dual counterparts of the … Read more
It has been known since the early 1970s that the Hessian matrices in quasi-Newton methods can be updated by variational means, in several different ways. The usual formulation of these variational problems uses a coordinate system, and the symmetry of the Hessian matrices are enforced as explicit constraints. As a result, the variational problems seem … Read more
The Lipschitz Global Optimizer (LGO) software integrates global and local scope search methods, to handle nonlinear optimization models. Here we discuss the LGO implementation linked to the General Algebraic Modeling System (GAMS). First we review the key features and basic usage of the GAMS /LGO solver option, then present reproducible numerical results to illustrate its … Read more
Wavelet decomposition problems have been modeled as linear programs – but only as extremely dense problems. Both revised simplex and interior point methods have difficulty with dense linear programs. The question then is how to get around that issue. In our experiments the standard method outperforms a revised implementation for these problems. Moreover, the standard … Read more
Two-step mixed-integer rounding inequalities are valid inequalities derived from a facet of a simple mixed-integer set with three variables and one constraint. In this paper we investigate how to effectively use these inequalities as cutting planes for general mixed-integer problems. We study the separation problem for single constraint sets and show that it can be … Read more
The convergence of primal and dual central paths associated to entropy and exponential functions, respectively, for semidefinite programming problem are studied in this paper. As an application, the proximal point method with the Kullback-Leibler distance applied to semidefinite programming problems is considered, and the convergence of primal and dual sequences is proved. Citation Journal of … Read more