Applied Mathematics and Optimization 

About: Applied Mathematics and Optimization is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Optimal control & Mathematics. It has an ISSN identifier of 0095-4616. Over the lifetime, 1844 publications have been published receiving 45133 citations. The journal is also known as: Applied mathematics optimization & Applied mathematics and optimization.

A Strong Maximum Principle for some quasilinear elliptic equations

Abstract: In its simplest form the Strong Maximum Principle says that a nonnegative superharmonic continuous function in a domain Ω ⊂ ℝ n ,n ⩾ 1, is in fact positive everywhere. Here we prove that the same conclusion is true for the weak solutions of − Δu + β(u) = f withβ a nondecreasing function ℝ → ℝ,β(0)=0, andf⩾0 a.e. in Ω if and only if the integral∫(β(s)s) −1/2 ds diverges ats=0+. We extend the result to more general equations, in particular to − Δ p u + β(u) =f where Δ p (u) = div(|Du| p-2 Du), 1

The internal model principle for linear multivariable regulators

Abstract: Necessary structural criteria are obtained for linear multivariable regulators which retain loop stability and output regulation in the presence of small perturbations, of specified types, in system parameters. It is shown that structural stability thus defined requires feedback of the regulated variable, together with a suitably reduplicated model, internal to the feedback loop, of the dynamic structure of the exogenous reference and disturbance signals which the regulator is required to process. Necessity of these structural features constitutes the ‘internal model principle’.

Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework

Abstract: This paper is concerned with a continuous-time mean-variance portfolio selection model that is formulated as a bicriteria optimization problem. The objective is to maximize the expected terminal return and minimize the variance of the terminal wealth. By putting weights on the two criteria one obtains a single objective stochastic control problem which is however not in the standard form due to the variance term involved. It is shown that this nonstandard problem can be ``embedded'' into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model proves to be an appropriate and effective framework to study the mean-variance problem in light of the recent development on general stochastic LQ problems with indefinite control weighting matrices. This gives rise to the efficient frontier in a closed form for the original portfolio selection problem.

Regularity and stability for the mathematical programming problem in Banach spaces

Abstract: This paper deals with a regularity assumption for the mathematical programming problem in Banach spaces. The attractive feature of our constraint qualification is the fact that it can be considered as a condition on the active part only of the constraint, and that it is preserved under small perturbations. Moreover, we show that our condition is “almost” equivalent to the existence of a non-empty and weakly compact set of Lagrange multipliers. The main step in the proof of our results is a generalization of the open mapping theorem.

On the pricing of American options

Abstract: The problem of valuation for contingent claims that can be exercised at any time before or at maturity, such as American options, is discussed in the manner of Bensoussan [1]. We offer an approach which both simplifies and extends the results of existing theory on this topic.