1 citations · 1 across the 7 of their papers we have counts for
8 papers
The Unified Separation Condition: A General Constraint Qualification for Smooth and Nonsmooth Optimization
Majid E. Abbasov
We introduce the Unified Separation Condition (USC) - a simple and general constraint qualification for finite-dimensional nonlinear programming. The USC requires that the origin b…
A Unified Regularity Condition for Optimal Control: Bridging LICQ, MFCQ, and Subdifferentials
Majid Abbasov
This paper presents a unified derivation of transversality conditions in optimal control problems using exact penalty functions. The key regularity condition is that the origin is…
Optimal 3D Road Alignment on Topographic Surfaces: A Convergent Dynamic Programming Approach
Majid E. Abbasov, Anna A. Gorbunova
We consider the problem of finding an optimal 3D road trajectory between two points on a terrain with variable elevation. Unlike common heuristic pathfinding methods, we propose a…
Regularization for the Approximation of 2D Set of Points via the Length of the Curve
Majid E. Abbasov, Anna I. Belenok
We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often proble…
Directional differentiability, coexhausters, codifferentials and polyhedral DC functions
Majid E. Abbasov
Codifferentials and coexhausters are used to describe nonhomogeneous approximations of a nonsmooth function. Despite the fact that coexhausters are modern generalizations of codiff…
Converting exhausters and coexhausters
Majid E. Abbasov
Exhausters and coexhausters are notions of constructive nonsmooth analysis which are used to study extremal properties of functions. An upper exhauster (coexhauster) is used to get…
Finding the set of global minimizers of a piecewise affine function
Majid E. Abbasov
In the present work we study a problem of finding a global minimum of a piecewise affine function. We employ optimality conditions for the problem in terms of coexhausters and use…
Optimality conditions for an exhausterable function on an exhausterable set
Majid Abbasov
Exhausters are families of convex compact sets that allow one to represent directional derivative of the studied function at the considered point in the form of InfMax or SupMin of…