Contingent derivatives and regularization for noncoercive inverse problems

We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map by using the first-order and the second-order contingent derivatives. We explore the inverse problem by using the output least-squares and the modified output least-squares objectives. By regularizing the non-coercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results

The Impact of Structural Reforms on Environmental Problems in Agriculture

With the technological advancement in almost every sphere of human life, there has been an increased tendency to focus on the conservation of scarce resources by acquiring higher levels of resource use efficiency in the production process. However, there also remains a visible element of haste in policy planning towards the achievement of these goals, particularly in the developing world. The economic viability of such haste would have been positive had this helped in reducing the social cost of delayed policy actions taken in the preceding period. Conversely, the policy planning efforts continue to be ignorant of long-term consequences of current actions, as well as deficient in integrating various components of the sector or sub-sector of the economy which can not be viewed in isolation. These design defects in policies are largely ignored in post-impact evaluations of programmes, and failures are often incorrectly attributed to implementation, or simply referred to as managerial snags. Nevertheless, these inherent design defects become the primary contributors towards non-sustainability of development programmes. Pakistan’s agriculture, with its declining share in the economy over time, is still the single largest sector accounting for 23 percent in the GDP. Whereas its share has steadily declined in favour of rising manufacturing and services sectors, its rate of growth has remained rather erratic.

Causality, Input Price Variability, and Structural Changes in the U.S. Livestock- Meat Industry

Industrial Organization, Livestock Production/Industries,

Mirror Symmetry and the Classification of Orbifold del Pezzo Surfaces

We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate mutation-equivalence classes of Fano polygons with Q-Gorenstein deformation classes of del Pezzo surfaces