Mean-field spin glasses are families of random energy functions (Hamiltonians) on high-dimensional product spaces. In this paper, we consider the case of Ising mixed p-spin models,;namely, Hamiltonians H-N : Sigma(N) ...
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Mean-field spin glasses are families of random energy functions (Hamiltonians) on high-dimensional product spaces. In this paper, we consider the case of Ising mixed p-spin models,;namely, Hamiltonians H-N : Sigma(N) -> R on the Hamming hypercube Sigma(N) = [+/- 1](N), which are defined by the property that {H-N(sigma)}(sigma is an element of Sigma N) is a centered Gaussian process with covariance E{H-N(sigma(1)) H-N(sigma(2))} depending only on the scalar product (sigma(1), sigma(2)). The asymptotic value of the optimum max(sigma is an element of Sigma N) H-N (sigma) was characterized in terms of a variational principle known as the Parisi formula, first proved by Talagrand and, in a more general setting, by Panchenko. The structure of superlevel sets is extremely rich and has been studied by a number of authors. Here, we ask whether a near optimal configuration sigma can be computed in polynomial time. We develop a message passing algorithm whose complexity per-iteration is of the same order as the complexity of evaluating the gradient of H-N, and characterize the typical energy value it achieves. When the p-spin model H-N satisfies a certain no-overlap gap assumption, for any epsilon > 0, the algorithm outputs sigma is an element of Sigma(N) such that H-N (sigma) >= (1 - epsilon) max(sigma') H-N (sigma'), with high probability. The number of iterations is bounded in N and depends uniquely on epsilon. More generally, regardless of whether the no-overlap gap assumption holds, the energy achieved is given by an extended variational principle, which generalizes the Parisi formula.
The analysis of dynamic systems is essential in the design of both classical and modern controllers, especially in situations where obtaining accurate model parameters is complex. This difficulty stems from the uncert...
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In this paper, we consider a generalized ranking and selection problem, where each system’s performance depends on a continuous decision variable necessitating optimization. We focus on a fixed confidence formulation...
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Subset selection is a fundamental problem across a wide range of applications. In this study, we explore scenarios where the variables within the original dataset are divided into distinct groups. Subsequently, we inv...
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In the paper, an fusion of optimized A∗ algorithm and Dynamic Window Approach (DWA) algorithm to pathfinding is presented, combining the strengths of both the A∗ and DWA algorithms. The innovation of the fusion algori...
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We propose an exact method that finds a minimum complete Pareto front of the biobjective minimum length minimum risk spanning trees problem. The method consists in two algorithms. The first algorithm finds a single mi...
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We study variants of the Optimal Refugee Resettlement problem where a set F of refugee families need to be allocated to a set P of possible places of resettlement in a feasible and optimal way. Feasibility issues emer...
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Intelligent Transportation Systems (ITS) paves the way towards a futuristic world. A systematic, quick and trouble-free transportation system is in demand for last-mile deliveries to support the logistic companies. Wi...
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Differential Evolution (DE) is a widely used optimization algorithm due to its robustness and simplicity as a population search technique. However, it can struggle to balance the trade-off between exploring and exploi...
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The previously proposed Newton observer for nonlinear systems has fast exponential convergence and applies to a wide class of problems. However, the Newton observer lacks robustness against measurement noise due to th...
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ISBN:
(纸本)9798350328066
The previously proposed Newton observer for nonlinear systems has fast exponential convergence and applies to a wide class of problems. However, the Newton observer lacks robustness against measurement noise due to the computation of a matrix inverse. In this paper, we propose a novel observer for discrete-time system with sampled measurements to alleviate the impact of measurement noise. The key to the proposed observer is an iterative pre-conditioning technique for the gradient-descent method, used previously for solving general optimization problems. The proposed observer utilizes a nonsymmetric pre-conditioner to approximate the observability mapping's inverse Jacobian so that it asymptotically replicates the Newton observer with an additional benefit of enhanced robustness against measurement noise. Our observer applies to a wide class of nonlinear systems, as it is not contingent upon linearization or any specific structure in the plant nonlinearity. Its improved robustness compared to the prominent nonlinear observers is demonstrated through empirical results.
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