Description:
Different stationarity and regularity concepts for extended real-valued functions on metric spaces are considered in the paper. The properties are characterized in terms of certain local constants. A classifcation scheme for stationarity/regularity constants and corresponding concepts is proposed. The relations between different constants are established.
Description:
Stationarity and regularity concepts for the three typical for variational analysis classes of objects - real-valued functions, collections of sets, and multifunctions - are investigated. An attempt is maid to present a classification scheme for such concepts and to show that properties introduced for objects from different classes can be treated in a similar way. Furthermore, in many cases the corresponding properties appear to be in a sense equivalent. The properties are defined in terms of certain constants which in the case of regularity properties provide also some quantitative characterizations of these properties. The relations between different constants and properties are discussed.
Description:
In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented.
Description:
In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented.
Description:
In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivative-like objects – slopes – are introduced and a classification scheme of error bound criteria is presented.
Description:
In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivative-like objects – slopes – are introduced and a classification scheme of error bound criteria is presented.
Description:
This article aims to demonstrate how the definitions of slopes can be extended to multi-valued mappings between metric spaces and applied for characterizing metric regularity. Several kinds of local and nonlocal slopes are defined and several metric regularity properties for set-valued mappings between metric spaces are investigated.
Description:
This article aims to demonstrate how the definitions of slopes can be extended to multi-valued mappings between metric spaces and applied for characterizing metric regularity. Several kinds of local and nonlocal slopes are defined and several metric regularity properties for set-valued mappings between metric spaces are investigated.
Description:
The Holder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extended real-valued functions of two variables. A classification scheme for the general Holder metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes.
Description:
The Holder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extended real-valued functions of two variables. A classification scheme for the general Holder metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes.
Description:
Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued functions of two variables. A classification scheme for the general error bound and metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes.
Description:
Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued functions of two variables. A classification scheme for the general error bound and metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes.
Description:
This paper sheds new light on regularity of multifunctions through various characterizations of directional Holder/Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Holder/Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional Holder/Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed.
Description:
This paper sheds new light on regularity of multifunctions through various characterizations of directional Holder/Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations, we show that directional Holder/Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional Holder/Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed.
Description:
The coast of Bangladesh is funnel shaped. The narrowing of the Meghna estuary along with its peculiar topography creates a funneling effect that has a large impact on surge response. In order to have an accurate estimation of surge levels, the impacts of the estuary should be treated with due importance. To represent in detail the real complexities of the estuary, a very high resolution is required, which in turn necessitates more computational cost. Considering the facts into account, a location specific vertically integrated shallow water model in cylindrical polar coordinates is developed in this study to foresee water levels associated with a storm. A one-way nested grid technique is used to incorporate coastal complicities with minimum cost. In specific, a fine mesh scheme (FMS) capable of incorporating coastal complexities with acceptable accuracy is nested into a coarse mesh scheme (CMS) covering up to 15°N latitude in the Bay of Bengal. The coastal and island boundaries are approximated through appropriate stair step representation and the model equations are solved by a conditionally stable semi-implicit finite difference technique using a structured C-grid. Numerical experiments are performed using the model to estimate water levels due to surge associated with the April 1991 and AILA, 2009 cyclones, which struck the coast of Bangladesh. Time series of tidal level is generated from an available tide table through a cubic spline interpolation method. The computed surge response is superimposed linearly with the generated time series of tidal oscillation to obtain the time series of total water levels. The model results exhibit a good agreement with observation and reported data.
Description:
The purpose of this paper is to discuss some of the highlights of the theory of metric regularity relative to a cone. For example, we establish a slope and some coderivative characterizations of this concept, as well as some stability results with respect to a Lipschitz perturbation.
Description:
The purpose of this paper is to discuss some of the highlights of the theory of metric regularity relative to a cone. For example, we establish a slope and some coderivative characterizations of this concept, as well as some stability results with respect to a Lipschitz perturbation.
Description:
This paper continues the study of `good arrangements' of collections of sets in normed spaces near a point in their intersection. Our aim is to study general nonlinear transversality properties. We focus on dual space (subdifferential and normal cone) necessary characterizations of these properties. As an application, we provide dual necessary conditions for the nonlinear extensions of the new transversality properties of a set-valued mapping to a set in the range space due to Ioffe.
Description:
The research was supported by the Australian Research Council, project DP160100854. The second author benefited from the support of the FMJH Program PGMO and from the support of EDF.
Description:
After a 26-mm precipitation in February 2014, noticeable ground movements were recorded on the north batter of Maddingley brown coal open pit, Victoria. To investigate the rainfall effect on the stability of the brown coal batter with opened cracks, a three-dimensional geologic model was developed, and the finite element program encoded in Plaxis 3D was employed to conduct a complex two-phase (fluid-solid) coupled numerical simulation. It was found that the simulated deformations were well agreed with the field survey data. There were ground movements along the length of cracks on both sides of the crack with larger movement towards the pit bottom. The coupled effect of hydrostatic forces from the crack in the rear of the batter and from the clay layer underlain the batter caused the block to slide, or batter failure. From the results, it revealed that both short-term high rainfall intensity precipitation and long enduring low rainfall intensity precipitation could cause the brown coal batter with opened cracks instable.
Description:
Australian Research Training Program (RTP) Scholarship Federation University Australia George Collins Memorial Scholarship.
Description:
After a 26-mm precipitation in February 2014, noticeable ground movements were recorded on the north batter of Maddingley brown coal open pit, Victoria. To investigate the rainfall effect on the stability of the brown coal batter with opened cracks, a three-dimensional geologic model was developed, and the finite element program encoded in Plaxis 3D was employed to conduct a complex two-phase (fluid-solid) coupled numerical simulation. It was found that the simulated deformations were well agreed with the field survey data. There were ground movements along the length of cracks on both sides of the crack with larger movement towards the pit bottom. The coupled effect of hydrostatic forces from the crack in the rear of the batter and from the clay layer underlain the batter caused the block to slide, or batter failure. From the results, it revealed that both short-term high rainfall intensity precipitation and long enduring low rainfall intensity precipitation could cause the brown coal batter with opened cracks instable.
Description:
Australian Research Training Program (RTP) Scholarship Federation University Australia George Collins Memorial Scholarship.