Search results for "Control and Optimization"
showing 10 items of 448 documents
Coupled fixed point, F-invariant set and fixed point of N-order
2010
In this paper, we establish some new coupled fixed point theorems in complete metric spaces, using a new concept of $F$-invariant set. We introduce the notion of fixed point of $N$-order as natural extension of that of coupled fixed point. As applications, we discuss and adapt the presented results to the setting of partially ordered cone metric spaces. The presented results extend and complement some known existence results from the literature.
Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis
2000
Our aim is to present sufficient conditions ensuring Hoffman's error bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations (variational inequalities), and sensitivity analysis and on other problems like Lipschitzian properties of polyhedral multivalued mappings as well as weak sharp minima or linear conditioning. We show how the information about our sufficient conditions can be used to provide a computable constant such that Hoffman's error bound holds. We also show that this error bound is nothing but the classical Farkas lemma for linear …
Fixed points and completeness on partial metric spaces
2015
Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of…
Property (gab) through localized SVEP
2015
In this article we study the property (gab) for a bounded linear operator T 2 L(X) on a Banach space X which is a stronger variant of Browder's theorem. We shall give several characterizations of property (gab). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gab) holds for large classes of operators and prove the stability of property (gab) under some commuting perturbations. 2010 Mathematics Subject Classication. Primary 47A10, 47A11; Secondary 47A53, 47A55.
An exact and efficient approach for computing a cell in an arrangement of quadrics
2006
AbstractWe present an approach for the exact and efficient computation of a cell in an arrangement of quadric surfaces. All calculations are based on exact rational algebraic methods and provide the correct mathematical results in all, even degenerate, cases. By projection, the spatial problem is reduced to the one of computing planar arrangements of algebraic curves. We succeed in locating all event points in these arrangements, including tangential intersections and singular points. By introducing an additional curve, which we call the Jacobi curve, we are able to find non-singular tangential intersections. We show that the coordinates of the singular points in our special projected plana…
Farkas-Minkowski systems in semi-infinite programming
1981
The Farkas-Minkowski systems are characterized through a convex cone associated to the system, and some sufficient conditions are given that guarantee the mentioned property. The role of such systems in semi-infinite programming is studied in the linear case by means of the duality, and, in the nonlinear case, in connection with optimality conditions. In the last case the property appears as a constraint qualification.
A general metric regularity in asplund banach spaces
1998
This paper establishes a simple and easily-applied criterion for determining whether a multivalued mapping is metrically regular relatively to a subset in the range space.
A Coupled Fixed Point Theorem in Fuzzy Metric Space Satisfying ϕ-Contractive Condition
2013
The intent of this paper is to prove a coupled fixed point theorem for two pairs of compatible and subsequentially continuous (alternately subcompatible and reciprocally continuous) mappings, satisfyingϕ-contractive conditions in a fuzzy metric space. We also furnish some illustrative examples to support our results.
Minimum power losses by using droop coefficients regulation method with voltage and frequency constraints in islanded microgrids
2018
In this paper, a droop coefficients regulation methodology is proposed for an islanded microgrid to optimize the power losses. Based on the P-f and Q-V relations to adjust the droop coefficients at every loading condition, the optimized operating set point generates minimum power losses operation while satisfying the constraints of voltage and frequency limitation. A 9-bus case study is here implemented to show the effectiveness of this new approach as well as the improved operation quality of the system.
Reflections on the Hohmann Transfer
2004
Walter Hohmann was a civil engineer who studied orbital maneuvers in his spare time. In 1925, he published an important book (Ref. 1) containing his main result, namely, that the most economical transfer from a circular orbit to another circular orbit is achieved via an elliptical trajectory bitangent to the terminal orbits. With the advent of the space program some three decades later, the Hohmann transfer maneuver became the most fundamental maneuver in space. In this work, we present a complete study of the Hohmann transfer maneuver. After revisiting its known properties, we present a number of supplementary properties which are essential to the qualitative understanding of the maneuver.…