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We study a generalized vanishing discount problem for Hamilton--Jacobi equations, removing the standard monotonicity assumption, either in a global sense or when integrated against all Mather measures. Specifically, we consider \[ \lambda…
The main goal of this paper is to apply the machinery of variational analysis and generalized differentiation to study infinite horizon stochastic dynamic programming (DP) with discrete time in the Banach space setting without convexity…
Based on a fixed point argument, we give a {\it dynamical representation} of the viscosity solution to Cauchy problem of certain weakly coupled systems of Hamilton-Jacobi equations with continuous initial datum. Using this formula, we…
We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…
The aim of this work is to investigate the qualitative behaviour of a financial dynamical system which contains a time delay. We investigate the dynamic response of this system of which variables are interest rate, investment demand, price…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…
In this article, we address a class of non convex, integer, non linear mathematical programs using dynamic programming. The mathematical program considered, whose properties are studied in this article, may be used to model the optimal…
Here, we study the selection problem for the vanishing discount approximation of non-convex, first-order Hamilton-Jacobi equations. While the selection problem is well understood for convex Hamiltonians, the selection problem for non-convex…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
The author presented a stochastic and variational approach to the Lax-Friedrichs finite difference scheme applied to hyperbolic scalar conservation laws and the corresponding Hamilton-Jacobi equations with convex and superlinear…
We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…
We analyze an optimal stopping problem with a constraint on the expected cost. When the reward function and cost function are Lipschitz continuous in state variable, we show that the value of such an optimal stopping problem is a continuous…
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…
We establish a new regularity property for weak solutions of parabolic systems with coefficients depending measurably on time as well as on all spatial variables. Namely, weak solutions are locally H{\"o}lder continuous Lp valued functions…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
This paper discusses differential stability of convex programming problems in Hausdorff locally convex topological vector spaces. Among other things, we obtain formulas for computing or estimating the subdifferential and the singular…
Propositional dynamic logic (PDL) is an important modal logic used to specify and reason about the behavior of software. A challenging problem in the context of PDL is solving fixed-point equations, i.e., formulae of the form $x \equiv…
In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we…