Related papers: Potential Theory and Quadratic Programming

We consider Novikov's problem of describing level lines of quasiperiodic functions on a plane for two-dimensional potentials of dihedral symmetry. It is shown that quasiperiodic potentials of this type can have open level lines only at a…

We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely…

This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…

A recent model for the stock market calculates future price distributions of a stock as a wave function of a quantum particle confined in an infinite potential well. In such a model the question arose as to how to estimate the classical…

We define quasiconvex programming, a form of generalized linear programming in which one seeks the point minimizing the pointwise maximum of a collection of quasiconvex functions. We survey algorithms for solving quasiconvex programs either…

Aussel et al. (J Optim Theory Appl 170 818-837 2016) introduced the concept of projected solutions for the quasi-variational inequalities with a non-self constraint map, that is, the case where the constraint map may take values outside the…

The method for the recursive calculation of the effective potential is applied successfully in case of weak coupling limit (g tend to zero) to a multidimensional complex cubic potential. In strong-coupling limit (g tend to infinity), the…

We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…

In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…

Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer…

We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…

We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability…

A general approach for constructing multidimensional quasi-exactly solvable (QES) potentials with explicitly known eigenfunctions for two energy levels is proposed. Examples of new QES potentials are presented.

The potential energy problem in an electrostatically bound two-body system is studied in the framework of a recently proposed impact model of the electrostatic force and in analogy to the potential energy in a gravitationally bound system.…

We study the potential theory of a large class of infinite dimensional L\'evy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e. excessive functions with…

For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such kind of problems, we develop a general solution…

The problem of separation of variables in some coordinate systems obtained with the use of $L$-transformations is studied. Potentials are shown that allow separation of regular variables in a perturbed two-body problem. The potential…

A `polydisperse' system has an infinite number of conserved densities. We give a rational procedure for projecting its infinite-dimensional free energy surface onto a subspace comprising a finite number of linear combinations of densities…

The no-programming theorem prohibits the existence of a Universal Programmable Quantum Processor. This statement has several implications in relation to quantum computation, but also to other tasks of quantum information processing, making…

An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…