arXiv subjects

Behrooz Moosavi Ramezanzadeh

Publications and source records attributed to Behrooz Moosavi Ramezanzadeh.

7 recordsLinked to original sources

arXiv2026

An Asymptotic Mean Value Characterization for the Regularized $p$-Laplacian

We characterize solutions of the regularized $p$-Laplace equation \[ \operatorname{div}\!\left((1+|Dv|^2)^{p/2-1}Dv\right)=0, \qquad 1<p<\infty, \] in a bounded domain $Ω\subset\mathbb{R}^n$ by a pointwise asymptotic mean value identity. For $v\in C^2(Ω)$, solving the equation is equivalent to \[ v(x) = \frac{\widetildeα}{2} \left( \mathcal{S}_{\varepsilon}^{+}[v](x) + \mathcal{S}_{\varepsilon}^{-}[v](x) \right) + \widetildeβ \int_{B_\varepsilon(0)} v(x+h)ρ_\varepsilon(h)\,dh + o(\varepsilon^2), \] where \[ \widetildeα = \frac{p-2}{p+n+1}, \qquad \widetildeβ = \frac{n+3}{p+n+1}. \] The kernel $ρ_\varepsilon$ is the semicircular marginal of normalized Lebesgue measure on the $(n+1)$-dimensional ball, and $\mathcal{S}_{\varepsilon}^{+}$ and $\mathcal{S}_{\varepsilon}^{-}$ are the tilted strategic functionals arising from the affine lift \[ w(x,s)=v(x)+s. \] The lifted gradient $(Dv,1)$ never vanishes, so the extremal second-order expansion is valid at every gradient regime. The characterization holds for the full range $1<p<\infty$. By standard interior regularity for nondegenerate regularized $p$-growth equations, weak solutions are smooth in the interior; the weak and viscosity viewpoints for related quasilinear $p$-Laplace equations are connected in \cite{JLM01}. The convergence of the associated projected dynamic programming scheme is established in the companion paper \cite{Moosavi26}.

math.AP↗

arXiv2026

Partial Identification with Auxiliary Moment Restrictions

Partial identification is often set aside in practice because the identification regions it delivers are too wide to be useful, pushing researchers toward strong assumptions that buy point identification at the cost of credibility. We show that a source of information already sitting in most interval-valued datasets can fix this without adding any assumption at all. When an outcome is reported only as an interval---because a data custodian bracketed, top-coded, or formally privatized it to protect respondents---the same custodian typically continues to publish accurate population aggregates of that outcome, precisely because doing so does not compromise any individual record. We develop a framework for exploiting exactly this information: restricting the set of admissible completions of the data to those consistent with a known aggregate, rather than restricting the interval itself, and characterizing the sharp identification region that results for the best linear predictor. The restrictions we study behave in strikingly different ways---some collapse the region by a full dimension, others narrow it while leaving its shape intact. We characterize the geometric effect of each restriction and derive closed-form directional measures of identifying value for the mean and conditional-mean cases. An illustration using interval-valued wages from the Current Population Survey shows that the effect is far from marginal: modest auxiliary information recovers a substantial share of the identifying power usually thought to be lost once an outcome is coarsened.

econ.EM↗

arXiv2026

A Projected Tug-of-War Game for the Regularized $p$-Laplacian

We give a tug-of-war interpretation of the regularized $p$-Laplacian $\operatorname{div}\big((1+|Dv|^2)^{p/2-1}Dv\big)=0$ in a bounded domain $Ω\subset \mathbb{R}^n$, $p\ge 2$. The key is the linear lift $w(x,x_{n+1})=v(x)+x_{n+1}$, which identifies this equation with $Δ_p w=0$ in $\mathbb{R}^n+1$. Projecting the standard $(n+1)$-dimensional $p$-harmonious scheme onto $\mathbb{R}^n$ yields a discrete dynamic programming principle for which we prove existence, uniqueness, and Borel measurability of solutions with strip boundary data, identify the unique fixed point with the value of the projected game, and establish convergence to the viscosity solution as $\varepsilon\to 0$.

math.AP↗

arXiv2026

Public Good Provision under Locally Private Signals

We study public-good provision when a planner observes agents' preferences only through a fixed local-privacy channel that randomizes each report before it reaches the planner. We characterize the optimal reduced-form allocation: the project is implemented when an aggregate posterior score is positive, where each agent's score combines the posterior expected valuation and posterior virtual value. Privacy enters through these posterior objects, muting the responsiveness of provision to private preferences and, under weak monotone likelihood ratios, potentially generating pooling. We then distinguish the optimal reduced-form allocation from its implementation through signal-measurable transfers: the required transfers solve a Fredholm integral equation whose solution is unique under completeness when it exists, while existence requires a separate range condition. Maximum reduced-form revenue exhibits three population regimes: it is asymptotically linear, of square-root order, or exponentially small according as the lower endpoint of the valuation distribution is positive, zero, or negative. Finally, welfare comparisons depend on the privacy calibration. At a common noise scale, Laplace Blackwell-dominates logistic noise, while under a common tight $μ$-GDP calibration the ordering reverses for the maximally separated binary endpoint experiment. Thus the preferred privacy channel depends on the standard used to hold privacy fixed.

econ.TH↗

arXiv2026

Optimal Control of an Epidemic with Intervention Design

This paper investigates the optimal control of an epidemic governed by a SEIR model with an operational delay in vaccination. We address the mathematical challenge of imposing hard healthcare capacity constraints (e.g., ICU limits) over an infinite time horizon. To rigorously bridge the gap between theoretical constraints and numerical tractability, we employ a variational framework based on Moreau--Yosida regularization and establish the connection between finite- and infinite-horizon solutions via $Γ$-convergence. The necessary conditions for optimality are derived using the Pontryagin Maximum Principle, allowing for the characterization of boundary-maintenance arcs where the optimal strategy maintains the infection level precisely at the capacity boundary. Numerical simulations illustrate these theoretical findings, quantifying the shadow prices of infection and costs associated with intervention delays.

math.OC↗

arXiv2025

Beyond Scalars: Zonotope-Valued Utility for Representation of Multidimensional Incomplete Preferences(Incomplete Version)

In this paper, I propose a new framework for representing multidimensional incomplete preferences through zonotope-valued utilities, addressing the shortcomings of traditional scalar and vector-based models in decision theory. Traditional approaches assign single numerical values to alternatives, failing to capture the complexity of preferences where alternatives remainmain incomparable due to conflicting criteria across multiple dimensions. Our method maps each alternative to a zonotope, a convex geometric object in $\mathbb{R}^m$ formed by Minkowski sums of intervals, which encapsulates the multidimensional structure of preferences with mathematical rigor. The set-valued nature of these payoffs stems from multiple sources, including non-probabilistic uncertainty, such as imprecise utility evaluation due to incomplete information about criteria weights, and probabilistic uncertainty arising from stochastic decision environments. By decomposing preference relations into interval orders and utilizing an extended set difference operator, we establish a rigorous axiomatization that defines preference as one alternative's zonotope differing from another's within the non-negative orthant of $\mathbb{R}^m$. This framework generalizes existing representations and provides a visually intuitive and theoretically robust tool for modeling trade-offs among each dimension, while preferences are incomparable.

econ.TH↗

arXiv2025

Extended Set Difference : Inverse Operation of Minkowski Summation

This paper introduces the extended set difference, a generalization of the Hukuhara and generalized Hukuhara differences, defined for compact convex sets in $\mathbb{R}^d$. The proposed difference guarantees existence for any pair of such sets, offering a broader framework for set arithmetic. The difference may not be necessarily unique, but we offer a bound on the variety of solutions. The definition of the extended set difference is formulated through an optimization problem, which provides a constructive approach to its computation. The paper explores the properties of this new difference, including its stability under orthogonal transformations and its robustness to perturbations of the input sets. We propose a method to compute this difference through a formulated linear optimization problem.

math.OC↗