This paper studies the finite-horizon linear quadratic regulation problem where the dynamics of the system are assumed to be unknown and the state is accessible. Information on the system is given by a finite set of i...
详细信息
This paper studies the finite-horizon linear quadratic regulation problem where the dynamics of the system are assumed to be unknown and the state is accessible. Information on the system is given by a finite set of input-state data, where the input injected in the system is persistently exciting of a sufficiently high order. Using data, the optimal control law is then obtained as the solution of a suitable semidefinite program. The effectiveness of the approach is illustrated via numerical examples. Copyright (C) 2020 The Authors.
Standard interior point methods in semidefinite programming can be viewed as tracking a solution path for a homotopy defined by a system of bilinear equations. By considering this in the context of numerical algebraic...
详细信息
Standard interior point methods in semidefinite programming can be viewed as tracking a solution path for a homotopy defined by a system of bilinear equations. By considering this in the context of numerical algebraic geometry, we employ numerical algebraic geometric techniques such as adaptive precision path tracking, endgames, and projective space to accurately solve semidefinite programs. We develop feasibility tests for both primal and dual problems which can distinguish between the four feasibility types of semidefinite programs. Finally, we couple our feasibility tests with facial reduction to develop a solving approach that can handle every scenario arising in semidefinite programming, including problems with nonzero duality gap. Various examples are used to demonstrate the new methods with comparisons to commonly used semidefinite programming software. (C) 2021 The Author(s). Published by Elsevier B.V.
A mathematical optimization approach for the optimal operation focused on the economic dispatch for dc microgrid with high penetration of distributed generators and energy storage systems (ESS) via semidefinite progra...
详细信息
A mathematical optimization approach for the optimal operation focused on the economic dispatch for dc microgrid with high penetration of distributed generators and energy storage systems (ESS) via semidefinite programming (SDP) is proposed in this paper. The SDP allows transforming the nonlinear and non-convex characteristics of the economic dispatch problem into a convex approximation which is easy for implementation in specialized software, i.e., CVX. The proposed mathematical approach contemplates the efficient operation of a dc microgrid over a period of time with variable energy purchase prices, which makes it a practical methodology to apply in real-time operating conditions. A nonlinear autoregressive exogenous (NARX) model is employed for training an artificial neural network (ANN) for forecasting solar radiation and wind speed for renewable generation integration and dispatch considering periods of prediction of 0.5 h. Four scenarios are proposed to analyze the inclusion of ESS in a dc microgrid for economic dispatch studies. Additionally, the results are compared with GAMS commercial optimization package, which allows validating the accuracy and quality of the proposed optimizing methodology.
One of the downsides of the massive multiple-input-multiple-output (M-MIMO) system is its computational complexity. Considering that techniques and different algorithms proposed in the literature applied to convention...
详细信息
One of the downsides of the massive multiple-input-multiple-output (M-MIMO) system is its computational complexity. Considering that techniques and different algorithms proposed in the literature applied to conventional MIMO may not be well suited or readily applicable to M-MIMO systems, in this paper, the application of different formulations inside the convex optimization framework is investigated. This paper is divided into two parts. In the first part, linear programming, quadratic programming (QP), and semidefinite programming are explored in an M-MIMO environment with high-order modulation and under realistic channel conditions, i.e., considering spatial correlation, error in the channel estimation, as well as different system loading. The bit error rate is evaluated numerically through Monte Carlo simulations. In the second part, algorithms to solve the QP formulation are explored, and computational complexity in terms of floating-point operations (flops) is compared with linear detectors. Those algorithms have interesting aspects when applied to our specific problem (M-MIMO detection formulated as QP), such as the exploitation of the structure of the problem (simple constraints) and the improvement of the rate of convergence due to the well-conditioned Gram matrix (channel hardening). The number of iterations is higher when the number of users K becomes similar to the number of base station antennas M (i.e., K approximate to M) than the case K << M;the number of iterations increases slowly as the number of users K and base station antennas M increases while keeping a low system loading. The QP with projected algorithms presented better performance than minimum mean square error detector when K approximate to M and promising computational complexity for scenarios with increasing K and low system loading.
In this paper we consider covariance structural models with which we associate semidefinite programming problems. We discuss statistical properties of estimates of the respective optimal value and optimal solutions wh...
详细信息
In this paper we consider covariance structural models with which we associate semidefinite programming problems. We discuss statistical properties of estimates of the respective optimal value and optimal solutions when the 'true' covariance matrix is estimated by its sample counterpart. The analysis is based on perturbation theory of semidefinite programming. As an example we consider asymptotics of the so-called minimum trace factor analysis. We also discuss the minimum rank matrix completion problem and its SDP counterparts.
We propose a wide neighborhood primal-dual interior-point algorithm with arc-search for semidefinite programming. In every iteration, the algorithm constructs an ellipse and searches an epsilon-approximate solution of...
详细信息
We propose a wide neighborhood primal-dual interior-point algorithm with arc-search for semidefinite programming. In every iteration, the algorithm constructs an ellipse and searches an epsilon-approximate solution of the problem along the ellipsoidal approximation of the central path. Assuming a strictly feasible starting point is available, we show that the algorithm has the iteration complexity bound O (n(3/4) log X-0.S-0/epsilon) for the Nesterov-Todd direction, which is similar to that of the corresponding algorithm for linear programming. The numerical results show that our algorithm is efficient and promising.
Forn,d,wN, letA(n,d,w) denote the maximum size of a binary code of word lengthn, minimum distanced and constant weightw. Schrijver recently showed using semidefinite programming that A(23,8,11)=1288, and the second au...
详细信息
Forn,d,wN, letA(n,d,w) denote the maximum size of a binary code of word lengthn, minimum distanced and constant weightw. Schrijver recently showed using semidefinite programming that A(23,8,11)=1288, and the second author thatA(22,8,11)=672 andA(22,8,10)=616. Here we show uniqueness of the codes achieving these bounds. LetA(n,d) denote the maximum size of a binary code of word lengthn and minimum distanced. Gijswijt et al. showed thatA(20,8)=256. We show that there are several nonisomorphic codes achieving this bound, and classify all such codes with all distances divisible by 4.
In this paper, we propose an array pattern synthesis scheme using semidefinite programming (SDP) under array excitation power constraints. When an array pattern synthesis problem is formulated as an SDP problem, it is...
详细信息
In this paper, we propose an array pattern synthesis scheme using semidefinite programming (SDP) under array excitation power constraints. When an array pattern synthesis problem is formulated as an SDP problem, it is known that an additional rank-one constraint is generated inevitably and relaxed via semidefinite relaxation. If the solution to the relaxed SDP problem is not of rank one, then conventional SDP-based array pattern synthesis approaches fail to obtain optimal solutions because the additional rank-one constraint is not handled appropriately. To overcome this drawback, we adopted a bisection technique combined with a penalty function method. Numerical applications are presented to demonstrate the validity of the proposed scheme.
We propose a homogeneous primal-dual interior-point method to solve sum-of-squares optimization problems by combining nonsymmetric conic optimization techniques and polynomial interpolation. The approach optimizes dir...
详细信息
We propose a homogeneous primal-dual interior-point method to solve sum-of-squares optimization problems by combining nonsymmetric conic optimization techniques and polynomial interpolation. The approach optimizes directly over the sum-of-squares cone and its dual, circumventing the semidefinite programming (SDP) reformulation, which requires a large number of auxiliary variables when the degree of sum-of-squares polynomials is large. As a result, it has substantially lower theoretical time and space complexity than the conventional SDP-based approach as the degree increases. Although our approach avoids the SDP reformulation, an optimal solution to the semidefinite program can be recovered with little additional effort. Computational results confirm that the proposed method is several orders of magnitude faster than the SDP-based approach for optimization problems over high-degree sum-of-squares polynomials.
One of the difficult tasks in quantum computation is inventing efficient exact quantum algorithms, which are the quantum algorithms that output the correct answer with certainty on any input. We improve and generalize...
详细信息
One of the difficult tasks in quantum computation is inventing efficient exact quantum algorithms, which are the quantum algorithms that output the correct answer with certainty on any input. We improve and generalize the semidefinite programming (SDP) method of Montanaro et al. (Algorithmica 71:775-796, 2015) in order to evaluate exact quantum query complexities of partial functions. We present a more systematical approach to achieve the inspired result by Montanaro et al. for the function EXACT24, which is the Boolean function of 4 bits that output only when 2 of the input bits are equal to 1. The same approach also allows us to reduce the size of the ancilla space used by the algorithms that evaluate symmetric functions like EXACT36. We employ the generalized SDP to verify the complexities of the earliest and best known quantum algorithms in the literature, namely, Deutsch-Jozsa and Grover algorithms for a small number of input bits. We utilized the method to solve the weight decision problem of bit strings with lengths up to 10 bits and observed that the generalized SDP gives better exact quantum query complexities than the known methods. Finally, we test the method on some selected functions and demonstrate that they all exhibit quantum speedup.
暂无评论