Consider the utilization of a Lagrangian dual method which is convergent for consistent convex optimization problems. When it is used to solve an infeasible optimization problem, its inconsistency will then manifest itself through the divergence of the sequence of dual iterates. Will then the sequence of primal subproblem solutions still yield relevant information regarding the primal program? ...

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...

Thermal considerations play an increasingly important role in the design of new processors. Thermal concerns impact how chips are laid out, how quickly processors can be clocked, processor reliability, and how expensive the packaging is. Current production chips are often packaged to dissipate maximum typical power, rather than maximum absolute power. We investigate techniques which would allow...

A (n+1)-dimensional cosmological model with a set of scalar fields and antisymmetric (p+2)-form is considered. Some of scalar fields may have negative kinetic terms, i.e. they may describe “phantom” fields. For certain odd dimensions (D = 4m + 1 = 5, 9, 13, ...) and (p + 2)forms (p = 2m−1 = 1, 3, 5, ...) and non-exceptional dilatonic coupling vector ~λ we obtain cosmological-type solutions to t...

We provide a holographic description of the BMN matrix model and its 1/2 BPS vacua, e.g. the concentric fuzzy spheres, by dual IIA supergravity solutions. We apply the Polchinski-Strassler method to construct our solutions, due to the similarity of the vacuum structure of this model and the N = 1∗ theory. The dual solutions have brane configurations which are concentric shells of S-wrapped D2 b...

We construct a new class of supersymmetric surface operators in N = 4 SYM and find the corresponding dual supergravity solutions. We show that the insertion of the surface operator – which is given by a WZW model supported on the surface – appears by integrating out the localized degrees of freedom along the surface which arise microscopically from a D3/D7 brane intersection. Consistency requir...

Thermal considerations play an increasingly important role in the design of new processors. Thermal concerns impact how chips are laid out, how quickly processors can be clocked, processor reliability, and how expensive the packaging is. Current production chips are often packaged to dissipate maximum typical power, rather than maximum absolute power. We investigate techniques which would allow...

We study primal solutions obtained as a by-product of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the methods producing such solutions only asymptotically (i.e., in the limit as the number of subgradien...

Lagrangean dualization and subgradient optimization techniques are frequently used within the field of computational optimization for finding approximate solutions to large, structured optimization problems. The dual subgradient scheme does not automatically produce primal feasible solutions; there is an abundance of techniques for computing such solutions (via penalty functions, tangential app...

In this paper, we study methods for generating approximate primal solutions as a by-product of subgradient methods applied to the Lagrangian dual of a primal convex (possibly nondifferentiable) constrained optimization problem. Our work is motivated by constrained primal problems with a favorable dual problem structure that leads to efficient implementation of dual subgradient methods, such as ...