We consider the Robust Network Loading problem with splittable flows and demands that belong to the budgeted uncertainty set. We compare the optimal solution cost and computational cost of the problem when using static routing, volume routing, affine routing, and dynamic routing. For the first three routing types, we compare the compact formulation with a … Read more
A traffic matrix $D_1$ dominates a traffic matrix $D_2$ if any capacity reservation supporting $D_1$ supports $D_2$ as well. We prove that $D_3$ dominates $D_3+ \lambda(D_2-D_1)$ for any $\lambda\geq 0$ if $D_1$ dominates $D_2$. By the property , it is pointed out that the domains supported by different traffic matrices are isomorphic on the extended … Read more
The recent research on the CVRP is being slowed down by the lack of a good set of benchmark instances. The existing sets suff er from at least one of the following drawbacks: (i) became too easy for current algorithms; (ii) are too arti cial; (iii) are too homogeneous, not covering the wide range of characteristics found … Read more
A class of trust-region algorithms is developed and analyzed for the solution of optimization problems with nonlinear equality and inequality constraints. Based on composite-step trust region methods and a filter approach, the resulting algorithm also does not require the computation of exact Jacobians; only Jacobian vector products are used along with approximate Jacobian matrices. As … Read more
We consider the pricing problem faced by a retailer endowed with a finite inventory of a product offered over a finite planning horizon in an environment where customers are price-sensitive. The parameters of the product demand curve are fixed but unknown to the seller who only has at his disposal a history of sales data. … Read more
A general nonlinear regularity model for a set-valued mapping $F:X\times\R_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is considered using special iteration procedures, going back to Banach, Schauder, Lusternik and Graves. Namely, we revise the \emph{induction theorem} from Khanh, \emph{J. Math. Anal. Appl.}, 118 (1986) and employ it to obtain basic estimates for studying … Read more
The main goal of this paper is to develop applications of advanced tools of first-order and second-order variational analysis and generalized differentiation to the fundamental notion of full stability of local minimizers of general classes of constrained optimization and minimax problems. In particular, we derive second-order characterizations of full stability and investigate its relationships with … Read more
In this paper we discuss the global weak sharp minima property for vector optimization problems with polynomial data. Exploiting the imposed polynomial structure together with tools of variational analysis and a quantitative version of \L ojasiewicz’s gradient inequality due to D’Acunto and Kurdyka, we establish the H\”older type global weak sharp minima with explicitly calculated … Read more
In this paper, we present PSMG–Parallel Structured Model Generator–an efficient parallel implementation of a model generator for the structure conveying modelling language (SML[4]). Unlike the earlier proof-of-concept implementation presented with SML, PSMG does not depend on AMPL. The main purposes of PSMG are: to provide an easy to use framework for modelling and generating large … Read more
Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable or distributed algorithms, which often obtain … Read more