Characterizations of the Solution Sets of Generalized Convex Minimization Problems

2000 Mathematics Subject Classification: 90C26, 90C20, 49J52, 47H05, 47J20.

A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.

On Pareto Sets in Multi-Criteria Optimization

Здравко Д. Славов - В тази работа се разглеждат Паретовските решения в непрекъсната многокритериална оптимизация. Обсъжда се ролята на някои предположения, които влияят на характеристиките на Паретовските множества. Авторът се е опитал да премахне предположенията за вдлъбнатост на целевите функции и изпъкналост на допустимата област, които обикновено се използват в многокритериалната оптимизация. Резултатите са на базата на конструирането на ретракция от допустимата област върху Парето-оптималното множество.

On some Extremal Problems of Landau

2000 Mathematics Subject Classification: Primary: 42A05. Secondary: 42A82, 11N05.

On Majorization for Matrices

In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities for these differences.

Convex and exact games with non-transferable utility

We generalize exactness to games with non-transferable utility (NTU). A game is exact if for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We consider ve generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be uni¯ed under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of Π-balanced, totally Π-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another.

Uma interface para o controle de robôs móveis por intermédio de gestos

The main objective of this work was to enable the recognition of human gestures through the development of a computer program. The program created captures the gestures executed by the user through a camera attached to the computer and sends it to the robot command referring to the gesture. They were interpreted in total ve gestures made by human hand. The software (developed in C ++) widely used the computer vision concepts and open source library OpenCV that directly impact the overall e ciency of the control of mobile robots. The computer vision concepts take into account the use of lters to smooth/blur the image noise reduction, color space to better suit the developer's desktop as well as useful information for manipulating digital images. The OpenCV library was essential in creating the project because it was possible to use various functions/procedures for complete control lters, image borders, image area, the geometric center of borders, exchange of color spaces, convex hull and convexity defect, plus all the necessary means for the characterization of imaged features. During the development of the software was the appearance of several problems, as false positives (noise), underperforming the insertion of various lters with sizes oversized masks, as well as problems arising from the choice of color space for processing human skin tones. However, after the development of seven versions of the control software, it was possible to minimize the occurrence of false positives due to a better use of lters combined with a well-dimensioned mask size (tested at run time) all associated with a programming logic that has been perfected over the construction of the seven versions. After all the development is managed software that met the established requirements. After the completion of the control software, it was observed that the overall e ectiveness of the various programs, highlighting in particular the V programs: 84.75 %, with VI: 93.00 % and VII with: 94.67 % showed that the nal program performed well in interpreting gestures, proving that it was possible the mobile robot control through human gestures without the need for external accessories to give it a better mobility and cost savings for maintain such a system. The great merit of the program was to assist capacity in demystifying the man set/machine therefore uses an easy and intuitive interface for control of mobile robots. Another important feature observed is that to control the mobile robot is not necessary to be close to the same, as to control the equipment is necessary to receive only the address that the Robotino passes to the program via network or Wi-Fi.

Noise resilient discrete-time cross-relation sensor characterisation

In-situ characterisation of thermocouple sensors is a challenging problem. Recently the authors presented a blind characterisation technique based on the cross-relation method of blind identification. The method allows in-situ identification of two thermocouple probes, each with a different dynamic response, using only sampled sensor measurement data. While the technique offers certain advantages over alternative methods, including low estimation variance and the ability to compensate for noise induced bias, the robustness of the method is limited by the multimodal nature of the cost function. In this paper, a normalisation term is proposed which improves the convexity of
the cost function. Further, a normalisation and bias compensation hybrid approach is presented that exploits the advantages of both normalisation and bias compensation. It is found that the optimum of the hybrid cost function is less biased and more stable than when only normalisation is applied. All results were verified by simulation.