Author

# Suchismita Tarafdar

Bio: Suchismita Tarafdar is an academic researcher from Shiv Nadar University. The author has contributed to research in topic(s): Differentiable function & Nonlinear programming. The author has an hindex of 6, co-authored 11 publication(s) receiving 63 citation(s).

##### Papers

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TL;DR: It is shown that the class of Lipschitz functions provides a suitable framework for the generalization of classical envelope theorems for a broad class of constrained programs relevant to economic models, in which nonconvexities play a key role, and where the primitives may not be continuously differentiable.

Abstract: We show in this paper that the class of Lipschitz functions provides a suitable framework for the generalization of classical envelope theorems for a broad class of constrained programs relevant to economic models, in which nonconvexities play a key role, and where the primitives may not be continuously differentiable. We give sufficient conditions for the value function of a Lipschitz program to inherit the Lipschitz property and obtain bounds for its upper and lower directional Dini derivatives. With strengthened assumptions we derive sufficient conditions for the directional differentiability, Clarke regularity, and differentiability of the value function, thus obtaining a collection of generalized envelope theorems encompassing many existing results in the literature. Some of our findings are then applied to decision models with discrete choices, to dynamic programming with and without concavity, to the problem of existence and characterization of Markov equilibrium in dynamic economies with nonconvexities, and to show the existence of monotone controls in constrained lattice programming problems.

6 citations

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TL;DR: In this article, a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or non-smooth objectives was developed.

Abstract: We develop a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or nonsmooth objectives. Our methods emphasize the role of the Strict Mangasarian–Fromovitz Constraint Qualification (SMFCQ), and include envelope theorems for both the convex and nonconvex case, allow for noninterior solutions as well as equality and inequality constraints. We give new sufficient conditions for the value function to be directionally differentiable, as well as continuously differentiable. We apply our results to stochastic growth models with Markov shocks and constrained lattice programming problems. (This abstract was borrowed from another version of this item.)

5 citations

01 Jan 2013

TL;DR: In this paper, the value function of a nonconvex and nonsmooth Lipschitz program was shown to be locally locally localizable, and bounds for upper and lower Dini derivatives of this value function were obtained.

Abstract: We develop new envelope theorems for a broad class of parameterized nonsmooth optimization problems typical of economic applications where nonconvexities play a key role. We provide su¢ cient conditions for the value function of a nonconvex and nonsmooth Lipschitz program to be locally Lipschitz. We obtain bounds for upper and lower Dini derivatives of this value function, as well as su¢ cient conditions for the

3 citations

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TL;DR: In this paper, the authors build a small open economy RBC model with financial frictions to analyze the incidence of expansionary fiscal consolidations in emerging market economies and calibrate the model to India, a proto-typical EME.

Abstract: We build a small open economy RBC model with financial frictions to analyze the incidence of expansionary fiscal consolidations in emerging market economies (EMEs). We calibrate the model to India, a proto-typical EME. We show that a spending based fiscal consolidation has an expansionary effect on output. In contrast, tax based consolidations are always contractionary. Either measure of consolidation, however, tends to increase the fiscal deficit and therefore the sovereign risk premia in our framework. Our findings support the results in the IMF WEO (2010), that tax based consolidation measures are more costly (in terms of GDP losses) than spending based consolidations in the short run. We identify new mechanisms that underlie the dynamics of fiscal reforms and their implications for successful fiscal consolidations.

1 citations

01 Jan 2012

TL;DR: In this paper, a generalized approach to envelope theorems that applies across a broad class of parameterized nonlinear optimization problems that arise typically in economic applications is developed. But the approach is limited to the case where the value function is locally Lipschitz and/or Clarke.

Abstract: We develop a generalized approach to envelope theorems that applies across a broad class of parameterized nonlinear optimization problems that arise typically in economic applications. In particular, we provide su¢ cient conditions under which the value function for a nonconvex, and/or nonsmooth program is locally Lipschitz and/or Clarke �

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01 Jan 1985

TL;DR: The first group of results in fixed point theory were derived from Banach's fixed point theorem as discussed by the authors, which is a nice result since it contains only one simple condition on the map F, since it is easy to prove and since it nevertheless allows a variety of applications.

Abstract: Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.

888 citations

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TL;DR: In this article, all Matlab and C++ programs necessary to produce the results of the article were described and a spreadsheet with Mexican data was also provided, along with a spreadsheet containing Mexican data.

Abstract: All Matlab and C++ programs necessary to produce the results of the article. There is also a Excel spreadsheet with Mexican data.

150 citations