arXiv subjects

Hongyi Jiang

Publications and source records attributed to Hongyi Jiang.

At least 19 recordsLinked to original sources

arXiv2026

Particle productions during collisions of highly boosted bubble walls

We investigate the production of particles much heavier than the characteristic scale of a cosmological first-order phase transition through collisions of highly boosted bubble walls. Using the scalar order-parameter field, we derive the ultraviolet behavior of its Fourier-space profile for both elastic and inelastic collisions. In the regime $\chi\equiv\omega^2-\mathbf{k}^2\gg M_h^2$, we find the universal result $\tilde{\phi}(\chi) = -2V^\prime(2v_\phi)\chi^{-2}+O(\chi^{-3}),$ implying that the spectral density scales as $F(\chi)\propto [V^\prime(2v_\phi)]^2\chi^{-4}$. Thus, heavy-particle production is localized near the instant of collision and, at leading order, depends on the scalar potential only through $V^\prime(2v_\phi)$. We verify this behavior using high-precision numerical solutions of the trapping equation, carefully suppressing spectral leakage from the finite integration domain, and obtain agreement over a broad ultraviolet range. We then derive analytical production rates for general heavy-particle thresholds and for fermion pairs, together with their cosmological number density and yield. Finally, we extend the analysis to $(3+1)$ dimensions and incorporate the finite bubble radius, finding an order-one suppression relative to the parallel-wall approximation. Our results revise the ultraviolet scaling used in previous treatments and have direct implications for superheavy dark-matter production and baryogenesis from bubble collisions.

hep-ph↗

arXiv2026

Sharp Logarithmic Thresholds for Cut Schedules in an Abstract Branch-and-Cut Model

Branch-and-cut interleaves branching with cutting-plane generation. How the two operations share the work of proving a bound is a basic theoretical question. We study an abstract model in which a tree certifies a target bound $Z$. Each branch node improves the bound by $\ell$ on one child and by $r$ on the other, where $0<\ell\le r$. The $i$th cut along a root-to-node path improves it by $c_i\ge0$, with cumulative improvement $C_k=\sum_{i=1}^k c_i$. Asymmetric branching enters through the rate $\lambda^{\star}>0$ defined by $e^{-\lambda^{\star}\ell}+e^{-\lambda^{\star}r}=1$. We establish uniform two-sided bounds of order $e^{\lambda^{\star}Z}$ on the minimal leaf count of pure branching trees. We then identify $\log k$ as the sharp threshold scale for the power of cutting. For cut schedules with extended limit $\gamma=\lim_{k\to\infty}C_k/\log k\in[0,\infty]$, minimal-size trees obey a trichotomy. If $\gamma=\infty$, cuts prove asymptotically all of the target. If $0\le\gamma<\infty$, the limiting fraction of the bound proved by cuts is $\gamma\lambda^{\star}/(1+\gamma\lambda^{\star})$. If $\gamma=0$, branch-and-cut has the same exponential size rate as pure branch-and-bound. This resolves open questions raised by Kazachkov, Le Bodic, and Sankaranarayanan on minimal-size trees under harmonically-worsening cuts, and generalizes their results to asymmetric branching and to all cut schedules in the model with this logarithmic limit. Finally, we show that branch-and-cut attains polynomial size in terms of $Z$ if and only if polynomially many cuts reduce the residual bound to $O(\log Z)$.

math.OC↗

arXiv2026

Promoting Fair Online Resource Allocation with Indivisible Units

Allocating scarce, indivisible resources to diverse groups under uncertainty is a central challenge in operations research, where efficiency-focused methods often underserve marginalized populations. We study the Fair Online Resource Allocation with Indivisible Units (FORA-IU) problem, in which an unpredictable sequence of demands must be served from a strictly fixed inventory, and ask what fairness guarantees are achievable under different distributional and structural assumptions. We adopt a fairness criterion based on the expected filling ratio (FE-FR-beta), which balances each group's expected allocation against its expected demand and priority weight. We design online policies that calibrate acceptance probabilities to the remaining budget, analyze both arbitrary time-varying and stationary arrivals, introduce the Random Cyclic Blocks (RCB) algorithm tailored to the stationary case, and study the effect of restricting policies to all-or-nothing allocations. For arbitrary time-varying arrivals, our policy achieves the optimal universal fairness guarantee of 1/(1+R_beta), where R_beta denotes the priority-weighted system load. For time-invariant arrivals, RCB achieves the exact finite-horizon guarantee [1-(1-R_beta/T)^T]/R_beta, which is at least (1-e^{-R_beta})/R_beta and is also tight. We further show that all-or-nothing allocation policies cannot match these guarantees. These findings demonstrate that distributional stationarity strictly improves the fairness frontier, and that partial fulfillment is a necessary condition for attaining optimal fairness in online indivisible resource allocation.

math.OC↗

arXiv2026

Robust Optimal Strategies for Early Liquidation in Financial Systems

We study the problem of asset liquidation in financial systems. During financial crises, asset liquidation is often inevitable but can lead to substantial losses if a significant amount of illiquid assets are sold simultaneously at depressed prices -- a phenomenon known as price impact. To tackle this challenge, we consider a two-period liquidation model that allows for early liquidation prior to clearing, thereby mitigating price impact at clearing, and we develop a worst-case approach to solve the decision-making problem on the optimal size of early liquidation. Specifically, we propose a robust optimal strategy -- a tractable liquidation approach that maximizes the worst-case value of liquid assets at clearing, taking into account the uncertainty of other banks' early liquidation decisions. We derive a (semi-)closed-form representation of this strategy in a practical scenario involving permanent price impact and analyze its sensitivity to that impact's magnitude. We further identify its closed-form expression in another practical scenario featuring interbank exposures. Our findings, although built upon a stylized model, offer valuable guidelines for developing robust liquidation strategies that mitigate losses resulting from asset liquidation.

q-fin.RM↗

arXiv2025

Smoothing Binary Optimization: A Primal-Dual Perspective

Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with large-scale instances. In this work, we introduce a novel primal-dual framework that reformulates unconstrained binary optimization as a continuous minimax problem, satisfying a strong max-min property. This reformulation effectively smooths the discrete problem, enabling the application of efficient gradient-based methods. We propose a simultaneous gradient descent-ascent algorithm that is highly parallelizable on GPUs and provably converges to a near-optimal solution in linear time. Extensive experiments on large-scale problems--including Max-Cut, MaxSAT, and Maximum Independent Set with up to 50,000 variables--demonstrate that our method identifies high-quality solutions within seconds, significantly outperforming state-of-the-art alternatives.

math.OC↗

arXiv2025

Optimal Micro-Transit Zoning via Clique Generation and Integer Programming

Micro-transit services offer a promising solution to enhance urban mobility and access, particularly by complementing existing public transit. However, effectively designing these services requires determining optimal service zones for these on-demand shuttles, a complex challenge often constrained by operating budgets and transit agency priorities. This paper presents a novel two-phase algorithmic framework for designing optimal micro-transit service zones based on the objective of maximizing served demand. A key innovation is our adaptation of the shareability graph concept from its traditional use in dynamic trip assignment to the distinct challenge of static spatial zoning. We redefine shareability by considering geographical proximity within a specified diameter constraint, rather than trip characteristics. In Phase 1, the framework employs a highly scalable algorithm to generate a comprehensive set of candidate zones. In Phase 2, it formulates the selection of a specified number of zones as a Weighted Maximum Coverage Problem, which can be efficiently solved by an integer programming solver. Evaluations on real-world data from Chattanooga, TN, and synthetic datasets show that our framework outperforms a baseline algorithm, serving 27.03% more demand in practice and up to 49.5% more demand in synthetic settings.

math.OC↗

arXiv2024

A Universal Transfer Theorem for Convex Optimization Algorithms Using Inexact First-order Oracles

Given any algorithm for convex optimization that uses exact first-order information (i.e., function values and subgradients), we show how to use such an algorithm to solve the problem with access to inexact first-order information. This is done in a ``black-box'' manner without knowledge of the internal workings of the algorithm. This complements previous work that considers the performance of specific algorithms like (accelerated) gradient descent with inexact information. In particular, our results apply to a wider range of algorithms beyond variants of gradient descent, e.g., projection-free methods, cutting-plane methods, or any other first-order methods formulated in the future. Further, they also apply to algorithms that handle structured nonconvexities like mixed-integer decision variables.

math.OC↗

arXiv2023

Approximation Algorithms for Line Planning with Heterogeneous Fleets and Multiple Resource Constraints

This paper studies line planning for urban bus networks that face multiple resource limits such as budget, labor, and emission caps while using heterogeneous fleets. The objective is to maximize total reward from serving passengers by assigning buses to candidate routes subject to capacity and resource constraints. The reward parameters are general and can encode diverse user preferences and multi-modal system configurations. Prior work typically assumes single resource constraints and homogeneous fleets, and often relies on methods that lack theoretical guarantees or computational tractability. We develop the first approximation algorithms with provable guarantees for this setting. For the cost-free variant, a randomized rounding scheme attains the optimal ratio $1-1/e$ which is tight unless $P = NP$. Leveraging this base algorithm, we derive extensions for the general case with arbitrary cost vectors, obtaining constant-factor approximation guarantees. To support large-scale application, we adapt the base algorithm to ensure computational scalability while preserving rigorous theoretical guarantees. Experiments on Greater Boston transit data demonstrate that our approach achieves 95\% to 98\% of the linear programming relaxation bound, whereas Gurobi solver fails on considerably smaller instances. Our experiments further show that heterogeneous fleets significantly outperform homogeneous ones and that multi-resource optimization is required to avoid significant resource limit violations, thereby underscoring the importance of our framework.

math.OC↗

arXiv2023

Testing Partial Instrument Monotonicity

When multi-dimensional instruments are used to identify and estimate causal effects, the monotonicity condition may not hold due to heterogeneity in the population. Under a partial monotonicity condition, which only requires the monotonicity to hold for each instrument separately holding all the other instruments fixed, the 2SLS estimand can still be a positively weighted average of LATEs. In this paper, we provide a simple nonparametric test for partial instrument monotonicity. We demonstrate the good finite sample properties of the test through Monte Carlo simulations. We then apply the test to monetary incentives and distance from results centers as instruments for the knowledge of HIV status.

econ.EM↗

arXiv2023

Information Complexity of Mixed-integer Convex Optimization

We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for the standard first-order oracle, improving upon the previous best known lower bound. This leaves only a lower order linear term (in the dimension) as the gap between the lower and upper bounds. This is derived as a corollary of a more fundamental ``transfer" result that shows how lower bounds on information complexity of continuous convex optimization under different oracles can be transferred to the mixed-integer setting in a black-box manner. Further, we (to the best of our knowledge) initiate the study of, and obtain the first set of results on, information complexity under oracles that only reveal \emph{partial} first-order information, e.g., where one can only make a binary query over the function value or subgradient at a given point. We give algorithms for (mixed-integer) convex optimization that work under these less informative oracles. We also give lower bounds showing that, for some of these oracles, every algorithm requires more iterations to achieve a target error compared to when complete first-order information is available. That is, these oracles are provably less informative than full first-order oracles for the purpose of optimization.

math.OC↗

arXiv2023

A Nonparametric Test of $m$th-degree Inverse Stochastic Dominance

This paper proposes a nonparametric test for $m$th-degree inverse stochastic dominance which is a powerful tool for ranking distribution functions according to social welfare. We construct the test based on empirical process theory. The test is shown to be asymptotically size controlled and consistent. The good finite sample properties of the test are illustrated via Monte Carlo simulations. We apply our test to the inequality growth in the United Kingdom from 1995 to 2010.

econ.EM↗

arXiv2022

Approximation Algorithm for Generalized Budgeted Assignment Problems and Applications in Transportation Systems

Motivated by a transit line planning problem in transportation systems, we investigate the following capacitated assignment problem under a budget constraint. Our model involves $L$ bins and $P$ items. Each bin $l$ has a utilization cost $c_l$ and an $n_l$-dimensional capacity vector. Each item $p$ has an $n_l$-dimensional binary weight vector $r_{lp}$, where the $1$s in $r_{lp}$ (if any) appear in consecutive positions, and its assignment to bin $l$ yields a reward $v_{lp}$. The objective is to maximize total rewards through an assignment that satisfies three constraints: (i) the total weights of assigned items do not violate any bin's capacity; (ii) each item is assigned to at most one open bin; and (iii) the overall utilization costs remain within a total budget $B$. We propose the first randomized rounding algorithm with a constant approximation ratio for this problem. We then apply our framework to the motivating transit line planning problem, presenting corresponding models and conducting numerical experiments using real-world data. Our results demonstrate significant improvements over previous approaches in addressing this critical transportation challenge.

math.OC↗

arXiv2022

Helly systems and certificates in optimization

Inspired by branch-and-bound and cutting plane proofs in mixed-integer optimization and proof complexity, we develop a general approach via Hoffman's Helly systems. This helps to distill the main ideas behind optimality and infeasibility certificates in optimization. The first part of the paper formalizes the notion of a certificate and its size in this general setting. The second part of the paper establishes lower and upper bounds on the sizes of these certificates in various different settings. We show that some important techniques existing in the literature are purely combinatorial in nature and do not depend on any underlying geometric notions.

math.OC↗

arXiv2021

Two-halfspace closure

We define a new cutting plane closure for pure integer programs called the two-halfspace closure. It is a natural generalization of the well-known Chvátal-Gomory closure. We prove that the two-halfspace closure is polyhedral. We also study the corresponding $2$-halfpsace rank of any valid inequality and show that it is at most the split rank of the inequality. Moreover, while the split rank can be strictly larger than the two-halfspace rank, the split rank is at most twice the two-halfspace rank. A key step of our analysis shows that the split closure of a rational polyhedron can be obtained by considering the split closures of all $k$-dimensional (rational) projections of the polyhedron, for any fixed $k\geq 2$. This result may be of independent interest.

math.OC↗

arXiv2021

Enumerating integer points in polytopes with bounded subdeterminants

We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial in the dimension and encoding size of the polytope. This extends a previous result by Artmann et al. who showed that integer linear optimization in such polytopes can be done in polynomial time.

math.CO↗

arXiv2021

Complexity of branch-and-bound and cutting planes in mixed-integer optimization -- II

We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut framework can be orders of magnitude more efficient than employing these tools on their own. In particular, we give general conditions under which a cutting plane strategy and a branching scheme give a provably exponential advantage in efficiency when combined into branch-and-cut. The efficiency of these algorithms is evaluated using two concrete measures: number of iterations and sparsity of constraints used in the intermediate linear/convex programs. To the best of our knowledge, our results are the first mathematically rigorous demonstration of the superiority of branch-and-cut over pure cutting planes and pure branch-and-bound.

math.OC↗

arXiv2020

Complexity of branch-and-bound and cutting planes in mixed-integer optimization

We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of disjunctions. We extend a result of Dash to the nonlinear setting which shows that for convex 0/1 problems, CP does at least as well as BB, with variable disjunctions. We sharpen this by giving instances of the stable set problem where we can provably establish that CP does exponentially better than BB. We further show that if one moves away from 0/1 sets, this advantage of CP over BB disappears; there are examples where BB finishes in O(1) time, but CP takes infinitely long to prove optimality, and exponentially long to get to arbitrarily close to the optimal value (for variable disjunctions). We next show that if the dimension is considered a fixed constant, then the situation reverses and BB does at least as well as CP (up to a polynomial blow up), no matter which family of disjunctions is used. This is also complemented by examples where this gap is exponential (in the size of the input data).

math.OC↗

arXiv2020

Split cuts in the plane

We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.

math.OC↗