HIGHER-ORDER VARIATIONAL SETS, VARIATINAL DERIVATIVES AND HIGHER-ORDER NECESSARY CONDITIONS IN ABSTRACT MATHEMATICAL PROGRAMMING

Higher Order Variational Problems

Higher order variational problems appear often in the engineering literature and in connection with the so-called gradient theories of phase transitions within elasto-plastic regimes. The study of equilibria of micromagnetic materials asks for mastery of second order energies (see [51], [91]; see also [31], [38], [44], [45], [61], [77], [78], [79], [108]), and the Blake-Zisserman model for imag...

Multiobjective Duality in Variational Problems with Higher Order Derivatives

A multiobjective variational problem involving higher order derivatives is considered and optimality conditions for this problem are derived. A Mond-Weir type dual to this problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the al...

Higher Order Imperative Programming

It is argued that a programming style based on higher order techniques the use of procedures that have other procedures as arguments and or results can be most e ectively employed if it is driven by abstraction from real algorithms rather than attempting to work with a xed set of functional forms and the use of imperative forms and mutative procedures is permitted even encour aged rather than r...

Higher-Order Logic Programming

Higher-order Multidimensional Programming

We present a higher-order functional language in which variables define arbitrary-dimensional entities, where any atomic value may be used as a dimension, and a multidimensional runtime context is used to index the variables. We give an intuitive presentation of the language, present the denotational semantics, and demonstrate how function applications over these potentially infinite data struc...