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Advances in Mathematical Methods in Optimal Control and Applications, 2nd...
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Advances in Mathematical Methods in Optimal Control and Applications, 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 August 2026 | Viewed by 1008

Editor

Dr. Cristiana J. Silva

E-Mail Website
Guest Editor
Department of Mathematics, ISTA, Instituto Universitário de Lisboa (ISCTE-IUL), Av. das Forças Armadas, 1649-026 Lisbon, Portugal
Interests: optimal control theory; mathematical modeling; optimization methods; applications to biology and epidemiology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Optimal control theory is a mathematical research area of great development with a wide range of applications across various fields. Optimal control problems aim to find the optimal control strategy that minimizes an objective (also called cost) function, while satisfying control system dynamics and a set of constraints (e.g., boundary, state, and control). The mathematical framework of the control system, cost function, and constraints can be very different, and, for each of them, distinct mathematical methods must be applied.

This Special Issue focuses on recent advances in mathematical methods for the optimal control of different types of control systems, state and control constraints, and boundary conditions. We welcome papers on new mathematical methods for optimal control problems with applications in biology, ecology, population dynamics, epidemiology, economics, etc.

Dr. Cristiana J. Silva
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • optimal control problems
  • optimality conditions
  • mathematical methods
  • applications

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Published Papers (1 paper)

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Research

30 pages, 17844 KB  
Article
Hysteresis and Optimal Pricing of Subscriptions with Cancellation Cost
by Dmitrii Rachinskii
Axioms 2026, 15(7), 506; https://doi.org/10.3390/axioms15070506 - 5 Jul 2026
Viewed by 326
Abstract
We develop a stochastic Stackelberg model of a subscription market with cancellation costs. A representative consumer chooses when to subscribe to and cancel a service as the utility derived from the subscription evolves according to a diffusion process, while the firm selects the [...] Read more.
We develop a stochastic Stackelberg model of a subscription market with cancellation costs. A representative consumer chooses when to subscribe to and cancel a service as the utility derived from the subscription evolves according to a diffusion process, while the firm selects the subscription fee and cancellation cost to maximize its expected payoff. The consumer’s problem is equivalent to the classical real-options model of entry and exit under uncertainty with adjustment costs and exhibits a two-threshold policy with an inaction band and hysteresis. Unlike the standard formulation, in which the optimal thresholds are characterized implicitly through a system of nonlinear equations, we derive an explicit parametric solution in closed form. This solution reduces the firm’s optimization problem to a two-dimensional unconstrained problem and yields a detailed characterization of the optimal pricing policy. We show that the firm’s strategy exhibits three qualitatively distinct regimes depending on the initial utility level. For small utility levels, the optimal cancellation cost is zero. In an intermediate regime, the firm’s optimal policy induces the consumer to set the entry threshold equal to the initial utility level, resulting in immediate subscription. For sufficiently large utility levels, the firm induces permanent lock-in by setting a high cancellation cost and a low subscription fee: the consumer subscribes immediately and never subsequently unsubscribes. The transition between the latter two regimes is discontinuous and results from competition between two local maxima of the firm’s payoff function. We then extend the model to a heterogeneous population of consumers. The superposition of individual two-threshold subscription strategies generates a Preisach hysteresis operator describing the aggregate dependence of the firm’s revenue on the utility dynamics. The discontinuous regime transition persists under heterogeneity, demonstrating the robustness of the underlying mechanism. The Preisach representation predicts complex history dependence and long-term effects of temporary utility shocks. For a gamma distribution of consumer preferences, the firm’s expected payoff is obtained in closed form in terms of incomplete gamma functions. Full article
(This article belongs to the Special Issue Advances in Mathematical Methods in Optimal Control and Applications, 2nd Edition)
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