arXiv subjects

Atsushi Hori

Publications and source records attributed to Atsushi Hori.

6 recordsLinked to original sources

arXiv2026

A Regularized Nikaido-Isoda Function Approach to Multi-Leader-Follower Games

A multi-leader--follower game (MLFG) is a hierarchical noncooperative game in which leaders compete at the upper level while taking into account the followers' best responses at the lower level. A typical approach to solving the MLFG reformulates it as an equilibrium problem with equilibrium constraints (EPECs) by replacing the lower-level game with its KKT conditions. Another approach, when each follower's response is unique, is to reformulate the MLFG as a Nash equilibrium problem by substituting these response functions into each leader's problem. However, both reformulations may lack scalability since higher-order derivatives may be required when solving the resulting problems. In this paper, we propose a new reformulation of the MLFG by exploiting a regularized Nikaido--Isoda function and approximating the MLFG by a single-level differentiable Nash equilibrium problem with a penalty parameter. The proposed reformulation neither requires derivative information on the followers' game nor assumes convexity of each follower's problem; hence, it can handle a broader class of MLFGs. Under global subanalyticity, we analyze the mathematical relationship between equilibria of the original MLFG and the proposed reformulation.

math.OC↗

arXiv2026

A closer target setting approach to boundary problems with the Russell graph measure

A Russell graph measure (RGM) is one of the standard DEA models, but its efficiency measure is not well-defined--or has unacceptable properties--at the boundary of the nonnegative orthant. This is known as a boundary problem. Existing studies have tackled this issue; however, their models may fail to identify an efficient target or fail to satisfy some desirable properties of efficiency measures. In this paper, we incorporate a closer target setting approach into the RGM model with production trade-offs to overcome such issues. We demonstrate that the efficiency measure of the proposed model overcomes the boundary problem and has stronger properties than existing models. We also demonstrate that the efficiency scores of the proposed model can be computed by solving a series of LPs. We conduct a numerical experiment with a real-world dataset to illustrate how targets provided by our model are realistic compared with the existing model, which also suggests the validity of our model in applications.

math.OC↗

arXiv2024

Variants of the slacks-based measure with assurance region and zeros in input-output data

Incorporating an assurance region (AR) into the slacks-based measure (SBM) improves practicality; however, its efficiency measure may not have desirable properties, such as monotonicity. We incorporate a closer target setting approach into the SBM with AR and a variant of the SBM with AR. We demonstrate that the efficiency measure with the hybrid approach has the same desirable properties as that without AR, and we also show that the efficiency scores can be computed by solving linear programming problems. Our proposed approach can handle zeros in the observed input-output data without any data transformation or additional model modification.

math.OC↗

arXiv2024

A method for multi-leader-multi-follower games by smoothing the followers' response function

The multi-leader--multi-follower game (MLMFG) involves two or more leaders and followers and serves as a generalization of the Stackelberg game and the single-leader--multi-follower game (SLMFG). Although MLMFG covers wide range of real-world applications, its research is still sparse. Notably, fundamental solution methods for this class of problems remain insufficiently established. A prevailing approach is to recast the MLMFG as an equilibrium problem with equilibrium constraints (EPEC) and solve it using a solver. Meanwhile, interpreting the solution to the EPEC in the context of MLMFG may be complex due to shared decision variables among all leaders, followers' strategies that each leader can unilaterally change, but the variables are essentially controlled by followers. To address this issue, we introduce a response function of followers' noncooperative game that is a function with leaders' strategies as a variable. Employing this approach allows the MLMFG to be solved as a single-level differentiable variational inequality using a smoothing scheme for the followers' response function. We also demonstrate that the sequence of solutions to the smoothed variational inequality converges to a stationary equilibrium of the MLMFG. Finally, we illustrate the behavior of the smoothing method by numerical experiments and confirm its validity.

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arXiv2023

Accelerating MPI Collectives with Process-in-Process-based Multi-object Techniques

In the exascale computing era, optimizing MPI collective performance in high-performance computing (HPC) applications is critical. Current algorithms face performance degradation due to system call overhead, page faults, or data-copy latency, affecting HPC applications' efficiency and scalability. To address these issues, we propose PiP-MColl, a Process-in-Process-based Multi-object Inter-process MPI Collective design that maximizes small message MPI collective performance at scale. PiP-MColl features efficient multiple sender and receiver collective algorithms and leverages Process-in-Process shared memory techniques to eliminate unnecessary system call, page fault overhead, and extra data copy, improving intra- and inter-node message rate and throughput. Our design also boosts performance for larger messages, resulting in comprehensive improvement for various message sizes. Experimental results show that PiP-MColl outperforms popular MPI libraries, including OpenMPI, MVAPICH2, and Intel MPI, by up to 4.6X for MPI collectives like MPI_Scatter and MPI_Allgather.

cs.DC↗

arXiv2023

Distributionally Robust Expected Residual Minimization for Stochastic Variational Inequality Problems

The stochastic variational inequality problem (SVIP) is an equilibrium model that includes random variables and has been widely applied in various fields such as economics and engineering. Expected residual minimization (ERM) is an established model for obtaining a reasonable solution for the SVIP, and its objective function is an expected value of a suitable merit function for the SVIP. However, the ERM is restricted to the case where the distribution is known in advance. We extend the ERM to ensure the attainment of robust solutions for the SVIP under the uncertainty distribution (the extended ERM is referred to as distributionally robust expected residual minimization (DRERM), where the worst-case distribution is derived from the set of probability measures in which the expected value and variance take the same sample mean and variance, respectively). Under suitable assumptions, we demonstrate that the DRERM can be reformulated as a deterministic convex nonlinear semidefinite programming to avoid numerical integration.

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