There are the notes of rather informal lectures given by the first co-author in UPMC, Paris, in January 2017. Practical goal is to explain how to compute or estimate the Morse index of the second variation. Symplectic geometry allows to effectively do it even for very degenerate problems with complicated constraints. Main geometric and analytic tool is the appropriately rearranged Maslov index....

A new method for refinement of 3D molecular structures by geometry optimization is presented. Prerequisites are a force field and a very fast procedure for the calculation of chemical shifts in every step of optimization. To the energy, provided by the force field (COSMOS force field), a pseudoenergy, depending on the difference between experimental and calculated chemical shifts, is added. In ...

In this paper, we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to the quadratic assignment problem. We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The latter formulation enables a hierarchy of approximations which r...

Optimization formulations seek to take advantage of structure and information in a particular problem, and investigate how successfully this information constrains the performance measures of interest. In this paper, we apply some recent results of algebraic geometry, to show how the underlying geometry of the problem may be incorporated in a natural way, in a semidefinite optimization formulat...

Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already few-atom systems. In this work, we introduce a variational quantum algorithm finding most stable structure molecule by explicitly considering parametric dependence electronic Hamiltonian on nuclear coordinates. The is obtained mini...

One primary problem in shape optimization of structures is making a robust link between design model (geometric description) and analysis model. This paper investigates the potential of Isogeometric Analysis (IGA) for solving this problem. The generic framework of shape optimization of structures is presented based on Isogeometric analysis. By discretization of domain via NURBS functions, the a...

an elliptical tank cross-section is formulated to explore and optimization method, based on a real-coded genetic algorithm to enhance the roll stability limit of a tank vehicle. a shape genetic algorithm optimization problem is applied to minimize the overturning moment imposed on the vehicle due to c.g. height of the liquid load, and lateral acceleration and cargo load shift . the minimization...