This paper describes a new approach to global optimization and
control uses geometric methods and modern quantum mathematics.
Polynomial extremal problems (PEP) are considered. PEP
constitute one of the most important subclasses of nonlinear
programming models. Their distinctive feature is that an objective
function and constraints can be expressed by polynomial functions
in one or several variables. A general approach to optimization
based on quantum holonomic computing algorithms and instanton
mechanism. An optimization method based on geometric Lie -
algebraic structures on Grassmann manifolds and related with Lax
type flows is proposed. Making use of the differential geometric
techniques it is shown that associated holonomy groups properly
realizing quantum computation can be effectively found concerning
polynomial problems. Two examples demonstrating calculation
aspects of holonomic quantum computer and maximum clique problems
in very large graphs,
are considered in detail.
It is known that leaf reflectance spectra can be used to estimate the contents of chemical components in vegetation. Recent novel applications include the detection of harmful biological agents that can originate from agricultural bioterrorism attacks. Such attacks have been identified as a major threat to the United States’ agriculture. Nevertheless, the usefulness of such approach is currently limited by distorting factors, in particular soil reflectance.
The quantitative analysis of the spectral curves from the reflection of plant leaves may be the basis for the development of new methods for interpreting the data obtained by the remote measurement of plants. We consider the problem of characterizing the chemical composition from noisy spectral data using an experimental optical method.
Using our experience in signal processing and optimization of complex systems we propose a new mathematical model for sensing of chemical components in vegetation. Estimates are defined as minimizers of penalized cost functionals with sequential quadratic programming (SQR) methods. A deviation measure used in risk analysis is also considered.
This framework is demonstrated for different agricultural plants using adaptive filtration, principal components analysis, and optimization techniques for classification of spectral curves of chemical components. Various estimation problems will be considered to illustrate the computational aspects of the proposed method.