Rate analysis of inexact dual first order methods: Application to distributed MPC for network systems

In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the cost using the Lagrange multipliers. The dual problem is solved by inexact first order methods based on approximate gradients and we prove sublinear rate of convergence for these methods. In particular, we provide, for the first time, estimates on the primal feasibility violation and primal and dual suboptimality of the generated approximate primal and dual solutions. Moreover, we solve approximately the inner problems with a parallel coordinate descent algorithm and we show that it has linear convergence rate. In our analysis we rely on the Lipschitz property of the dual function and inexact dual gradients. Further, we apply these methods to distributed model predictive control for network systems. By tightening the complicating constraints we are also able to ensure the primal feasibility of the approximate solutions generated by the proposed algorithms. We obtain a distributed control strategy that has the following features: state and input constraints are satisfied, stability of the plant is guaranteed, whilst the number of iterations for the suboptimal solution can be precisely determined.Comment: 26 pages, 2 figure

On linear convergence of a distributed dual gradient algorithm for linearly constrained separable convex problems

In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and Lipshitz continuity of the gradient of the primal objective function we have a global error bound type property for the dual problem. Using this error bound property we devise a fully distributed dual gradient scheme, i.e. a gradient scheme based on a weighted step size, for which we derive global linear rate of convergence for both dual and primal suboptimality and for primal feasibility violation. Many real applications, e.g. distributed model predictive control, network utility maximization or optimal power flow, can be posed as linearly constrained separable convex problems for which dual gradient type methods from literature have sublinear convergence rate. In the present paper we prove for the first time that in fact we can achieve linear convergence rate for such algorithms when they are used for solving these applications. Numerical simulations are also provided to confirm our theory.Comment: 14 pages, 4 figures, submitted to Automatica Journal, February 2014. arXiv admin note: substantial text overlap with arXiv:1401.4398. We revised the paper, adding more simulations and checking for typo

Surgical treatment of after scars excision wounds in children

Nicolae Testemitanu State University of Medicine and Pharmacy, Chisinau, Republic of Moldova, The 6th International Medical Congress for Students and Young Doctors, May 12-14, 2016Introduction: The ability of the primary wound healing, and hence the probability of formation of scar with favorable characteristics depends on how modern principles of surgery are implemented. Materials and methods: During last 3 years (2013-2015), in PMSI "Emilian Cotaga" Clinic, in the Department of burns, plastic and reconstructive surgery, 162 surgeries of scar excision and plasty with local tissues were performed.Results and discussions: Principles of surgical treatment of wounds are: (1) Preservation of blood supply in the tissue forming the wound wall at a satisfactory level. Solving a specific surgical task is always Associated with the separation of tissues, and in plastic surgery very often with the formation of skin-fat flaps. In cases when tissue blood flow does not have a distinct axial direction, the alimentation of the flap is considerably reduced. (2) Accurate approximation of the wound walls, especially of the skin edges. This presumes the presence of a relatively smooth and adequate, in terms of dimensions, to each other wound surfaces, which allows closing the wound or without cavities formation with a smooth surface in the area of sutures. (3) Fixing the wound edges in tight contact during the entire period of scar formation. (4) Minimal action of the sutures on the skin surface. If separate sutures are applied too tight, next to the suture develop small foci of necrosis, and the scar take a rail road appearance. This significantly impairs the external characteristics of the scar, and often makes it impossible for effective correction. Conclusion: It is necessary to apply the stitches so that after the operation would not remain any significant cavities in the wound that will increase the risk of infection. For this, first, wound layers must be precisely connected to the corresponding layers (muscle, fascia, subcutaneous fat, skin). The second important principle of wound closure: skin edges should be very close approximated by applying deep, subcutaneous stitches. This allows to close the wound with cutaneous sutures with a minimum tension, and thus with the lowest exposure of skin surface to sutures

A DECADE FROM THE MAJOR LAYOFFS IN THE JIU VALLEY

This essay is an overview of how the population of the largest coalfield of Romania Jiu Valley, the perceived major staff cuts in the mining industry, the solutions required for economic rehabilitation of the area and difficulties of everyday faced by residents of the region

Ultrasound Testing of Metallic Structures using a Dual Symmetric Path Inspection and a Matched Filter-based Method

International audienceIn this paper, we present a new technique for detecting and localising defects in metallic structures, using ultrasound non-destructive inspection. This technique consists in applying a dual path inspection and the matched filter to a stepped frequency-type signal. This new technique is compared with classical non-destructive testing approaches. An experimental setup is presented that allows us to validate the proposed method