This article deals with the problem of adaptive target detection in the presence of homogeneous Gaussian interference with frequency diverse array multiple-input multiple-output radar. Adaptive ...detectors are devised according to the generalized likelihood ratio test criterion, where the position of the target within each range cell is assumed unknown. To obtain the maximum likelihood estimate of the target incremental range under the H_1 hypothesis, three different optimization strategies are pursued. They are, respectively, based on semidefinite programming, discrete grid search, and Newton method. At the analysis stage, a detection performance comparison is carried on among the new proposed adaptive detectors, benchmark, and mismatched receivers. Numerical results corroborate the effectiveness of the developed receivers.
Let G be a graph with n vertices and m edges. One of several hierarchies towards the stability number of G is the exact subgraph hierarchy (ESH). On the first level it computes the Lovász theta ...function ϑ(G) as semidefinite program (SDP) with a matrix variable of order n+1 and n+m+1 constraints. On the kth level it adds all exact subgraph constraints (ESC) for subgraphs of order k to the SDP. An ESC ensures that the submatrix of the matrix variable corresponding to the subgraph is in the correct polytope. By including only some ESCs into the SDP the ESH can be exploited computationally.
In this paper we introduce a variant of the ESH that computes ϑ(G) through an SDP with a matrix variable of order n and m+1 constraints. We show that it makes sense to include the ESCs into this SDP and introduce the compressed ESH (CESH) analogously to the ESH. Computationally the CESH seems favorable as the SDP is smaller. However, we prove that the bounds based on the ESH are always at least as good as those of the CESH. In computational experiments sometimes they are significantly better.
We also introduce scaled ESCs (SESCs), which are a more natural way to include exactness constraints into the smaller SDP and we prove that including an SESC is equivalent to including an ESC for every subgraph.
•A new hierarchy for the stable set problem.•Theoretical investigation with respect to the exact subgraph hierarchy.•Computational comparison with the exact subgraph hierarchy.
Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control. To provide such a ...guarantee, one must be able to bound the output of neural networks when their input changes within a bounded set. In this article, we propose a semidefinite programming (SDP) framework to address this problem for feed-forward neural networks with general activation functions and input uncertainty sets. Our main idea is to abstract various properties of activation functions (e.g., monotonicity, bounded slope, bounded values, and repetition across layers) with the formalism of quadratic constraints. We then analyze the safety properties of the abstracted network via the S -procedure and SDP. Our framework spans the tradeoff between conservatism and computational efficiency and applies to problems beyond safety verification. We evaluate the performance of our approach via numerical problem instances of various sizes.
This paper addresses target localization problems in both noncooperative and cooperative 3-D wireless sensor networks (WSNs), for both cases of known and unknown sensor transmit power, i.e., PT . We ...employ a hybrid system that fuses distance and angle measurements, extracted from the received signal strength and angle-of-arrival information, respectively. Based on range and angle measurement models, we derive a novel nonconvex estimator based on the least squares criterion. The derived nonconvex estimator tightly approximates the maximum-likelihood estimator for small noise. We then show that the developed estimator can be transformed into a generalized trust region subproblem framework, by following the squared range approach, for noncooperative WSNs. For cooperative WSNs, we show that the estimator can be transformed into a convex problem by applying appropriate semidefinite programming relaxation techniques. Moreover, we show that the generalization of the proposed estimators for known PT is straightforward to the case where PT is not known. Our simulation results show that the new estimators have excellent performance and are robust to not knowing PT . The new estimators for noncooperative localization significantly outperform the existing estimators, and our estimators for cooperative localization show exceptional performance in all considered settings.
In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a ...less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. We exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.
•Scalable algorithm for variational quantum embedding, a semidefinite relaxation of the ground-state eigenvalue problem.•Alternates the solution of parallelizable local effective subproblems with global dual update steps.•Achieves convergence in number of iterations independent of cluster and system sizes.•Exploits translation invariance to efficiently project global matrix to the semidefinite cone.
To ensure grid efficiency and reliability, power system operators continuously monitor the operational characteristics of the grid through a critical process called state estimation (SE), which ...performs the task by filtering and fusing various measurements collected from grid sensors. This study analyzes the vulnerability of the key operation module, namely ac-based SE, against potential cyber attacks on data integrity, also known as false data injection attack (FDIA). A general form of FDIA can be formulated as an optimization problem, whose objective is to find a stealthy and sparse data injection vector on the sensor measurements with the aim of making the state estimate spurious and misleading. Due to the nonlinear ac measurement model and the cardinality constraint, the problem includes both continuous and discrete nonlinearities. To solve the FDIA problem efficiently, we propose a novel convexification framework based on semidefinite programming (SDP). By analyzing a globally optimal SDP solution, we delineate the "attackable region" for any given set of measurement types and grid topology, where the spurious state can be falsified by FDIA. Furthermore, we prove that the attack is stealthy and sparse, and derive performance bounds. Simulation results on various IEEE test cases indicate the efficacy of the proposed convexification approach. From the grid protection point of view, the results of this study can be used to design a security metric for the current practice against cyber attacks, redesign the bad data detection scheme, and inform proposals of grid hardening. From a theoretical point of view, the proposed framework can be used for other nonconvex problems in power systems and beyond.
In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cramér-Rao bound (CRB) as a performance metric ...of target estimation, under both point and extended target scenarios. We then propose minimizing the CRB of radar sensing while guaranteeing a pre-defined level of signal-to-interference-plus-noise ratio (SINR) for each communication user. For the single-user scenario, we derive a closed form for the optimal solution for both cases of point and extended targets. For the multi-user scenario, we show that both problems can be relaxed into semidefinite programming by using the semidefinite relaxation approach, and prove that the global optimum can be generally obtained. Finally, we demonstrate numerically that the globally optimal solutions are reachable via the proposed methods, which provide significant gains in target estimation performance over state-of-the-art benchmarks.
Quantum metrology is a rapidly developing branch of quantum technologies. While various theories have been established on quantum metrology for Markovian processes, i.e., quantum channel estimation, ...quantum metrology for non-Markovian processes is much less explored. In this Letter, we establish a general framework of non-Markovian quantum metrology. For any parametrized non-Markovian process on a finite-dimensional system, we derive a formula for the maximal amount of quantum Fisher information that can be extracted from it by an optimally controlled probe state. In addition, we design an algorithm that evaluates this quantum Fisher information via semidefinite programming. We apply our framework to noisy frequency estimation, where we find that the optimal performance of quantum metrology is better in the non-Markovian scenario than in the Markovian scenario and explore the possibility of efficient sensing via simple variational circuits.
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