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
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
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
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
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
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
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is rarely a systematic construction leading to the best possible formulation. We introduce embedding formulations and complexity as a new MIP … Read more
In this paper, we consider the polyhedral structure of the integrated minimum-up/-down time and ramping polytope for the unit commitment problem. Our studied generalized polytope includes minimum-up/-down time constraints, generation ramp-up/-down rate constraints, logical constraints, and generation upper/lower bound constraints. We derive strong valid inequalities by utilizing the structures of the unit commitment problem, and … Read more
We present a new Adaptive Regularization by Cubics (ARC) algorithm, which we name \arcq\ and which is very close in spirit to trust region methods, closer than the original ARC is. We prove global convergence to second-order critical points. We also obtain as a corollary the convergence of the original ARC method. We prove the … Read more