The Probabilistic Traveling Salesman Problem, introduced in 1985 by Jaillet, is one of the fundamental stochastic versions of the Traveling Salesman Problem: After the tour is chosen, each vertex is deleted with given probability 1-p. The eliminated vertices are bypassed which leads to shorter tours. The aim is to minimize the expected tour length. The … Read more
The Peaceman-Rachford splitting method is very efficient for minimizing sum of two functions each depends on its variable, and the constraint is a linear equality. However, its convergence was not guaranteed without extra requirements. Very recently, He et al. (SIAM J. Optim. 24: 1011 – 1040, 2014) proved the convergence of a strictly contractive Peaceman-Rachford … Read more
Recently the alternating direction method of multipliers (ADMM) has been widely used for various applications arising in scientific computing areas. Most of these application models are, or can be easily reformulated as, linearly constrained convex minimization models with separable nonlinear objective functions. In this note we show that ADMM can also be easily used for … Read more
We describe an iterative refinement procedure for computing extended precision or exact solutions to linear programming problems (LPs). Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are transformed only by modification … Read more
We show the validity of select existence results for a vector optimization problem, and a variational inequality. More generally, we consider generalized vector quasi-variational inequalities, as well as, fixed point problems on genuine Hadamard manifolds. ArticleDownload View PDF
With the need of 16/11nm cells, triple patterning lithography (TPL) has been concerned in lithography industry. Based on a new conflict projection technique to identify conflicts, we formulate in this paper the TPL layout decomposition problem as a minimum cost coloring problem. The problem is solved in two steps. First, it is relaxed to a … Read more
In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean (MAD). This makes it possible to use the old result of Ben-Tal … Read more
Direct-search algorithms form one of the main classes of algorithms for smooth unconstrained derivative-free optimization, due to their simplicity and their well-established convergence results. They proceed by iteratively looking for improvement along some vectors or directions. In the presence of smoothness, first-order global convergence comes from the ability of the vectors to approximate the steepest … Read more
We consider a parametric stochastic quasi-variational inequality problem (SQVIP for short) where the underlying normal cone is de ned over the solution set of a parametric stochastic cone system. We investigate the impact of variation of the probability measure and the parameter on the solution of the SQVIP. By reformulating the SQVIP as a natural equation … Read more
Many aspects of the classical price-setting newsvendor problem have been studied in the literature and most of the results pertain to the case where the price-demand relationship and demand distribution are explicitly provided. However, in practice, one needs to model and estimate these from historical sales data. Furthermore, many other drivers besides price must be … Read more