The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power *** complexity necessitates t...
详细信息
The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power *** complexity necessitates the employment of distributed solution methodologies,which are not only essential but also highly *** the realm of computational modelling,the multi-area economic dispatch problem(MAED)can be formulated as a linearly constrained separable convex optimization *** proximal point algorithm(PPA)is particularly adept at addressing such mathematical constructs *** study introduces parallel(PPPA)and serial(SPPA)variants of the PPA as distributed algorithms,specifically designed for the computational modelling of the *** PPA introduces a quadratic term into the objective function,which,while potentially complicating the iterative updates of the algorithm,serves to dampen oscillations near the optimal solution,thereby enhancing the convergence ***,the convergence efficiency of the PPA is significantly influenced by the parameter *** address this parameter sensitivity,this research draws on trend theory from stock market analysis to propose trend theory-driven distributed PPPA and SPPA,thereby enhancing the robustness of the computational *** computational models proposed in this study are anticipated to exhibit superior performance in terms of convergence behaviour,stability,and robustness with respect to parameter selection,potentially outperforming existing methods such as the alternating direction method of multipliers(ADMM)and Auxiliary Problem Principle(APP)in the computational simulation of power system dispatch *** simulation results demonstrate that the trend theory-based PPPA,SPPA,ADMM and APP exhibit significant robustness to the initial value of parameter c,and show superior convergence characteristics compared to the residual balancing ADMM.
In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions ...
详细信息
In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions separately. We also consider an approximate proximal point algorithm. Some properties of the ε-subdifferential and the ε-directional derivative are discussed. The convergence properties of the algorithms are established in both exact and approximate forms. Finally, we give some applications to the concave programming and maximum eigenvalue problems.
This paper deals with the proximal point algorithm for finding a singularity of sum of a single-valued vector field and a set-valued vector field in the setting of Hadamard manifolds. The convergence analysis of the p...
详细信息
This paper deals with the proximal point algorithm for finding a singularity of sum of a single-valued vector field and a set-valued vector field in the setting of Hadamard manifolds. The convergence analysis of the proposed algorithm is discussed. Applications to composite minimization problems and variational inequality problems are also presented.
In this work, we propose a proximalalgorithm for unconstrained optimization on the cone of symmetric semidefinite positive matrices. It appears to be the first in the proximal class on the set of methods that convert...
详细信息
In this work, we propose a proximalalgorithm for unconstrained optimization on the cone of symmetric semidefinite positive matrices. It appears to be the first in the proximal class on the set of methods that convert a Symmetric Definite Positive Optimization in Nonlinear Optimization. It replaces the main iteration of the conceptual proximal point algorithm by a sequence of nonlinear programming problems on the cone of diagonal definite positive matrices that has the structure of the positive orthant of the Euclidian vector space. We are motivated by results of the classical proximalalgorithm extended to Riemannian manifolds with nonpositive sectional curvature. An important example of such a manifold is the space of symmetric definite positive matrices, where the metrics is given by the Hessian of the standard barrier function -In det(X). Observing the obvious fact that proximalalgorithms do not depend on the geodesics, we apply those ideas to develop a proximal point algorithm for convex functions in this Riemannian metric. (c) 2009 Elsevier Inc. All rights reserved.
This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is cho...
详细信息
This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is chosen appropriately, the application of PPA could be effective to exploit the simplicity of the objective function. The resulting subproblems could be easier than those of the augmented Lagrangian method (ALM), a benchmark method for the model under our consideration. The efficiency of the customized application of PPA is demonstrated by some image processing problems.
It is a known fact that the method of alternating projections introduced long ago by von Neumann fails to converge strongly for two arbitrary nonempty, closed and convex subsets of a real Hilbert space. In this paper,...
详细信息
It is a known fact that the method of alternating projections introduced long ago by von Neumann fails to converge strongly for two arbitrary nonempty, closed and convex subsets of a real Hilbert space. In this paper, a new iterative process for finding common zeros of two maximal monotone operators is introduced and strong convergence results associated with it are proved. If the two operators are subdifferentials of indicator functions, this new algorithm coincides with the old method of alternating projections. Several other important algorithms, such as the contraction proximal point algorithm, occur as special cases of our algorithm. Hence our main results generalize and unify many results that occur in the literature. (C) 2012 Elsevier Ltd. All rights reserved.
We propose a Newton-CG primal proximal point algorithm (PPA) for solving large scale log-determinant optimization problems. Our algorithm employs the essential ideas of PPA, the Newton method, and the preconditioned C...
详细信息
We propose a Newton-CG primal proximal point algorithm (PPA) for solving large scale log-determinant optimization problems. Our algorithm employs the essential ideas of PPA, the Newton method, and the preconditioned CG solver. When applying the Newton method to solve the inner subproblem, we find that the log-determinant term plays the role of a smoothing term as in the traditional smoothing Newton technique. Focusing on the problem of maximum likelihood sparse estimation of a Gaussian graphical model, we demonstrate that our algorithm performs favorably compared to existing state-of-the-art algorithms and is much preferred when a high quality solution is required for problems with many equality constraints.
This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic O(1/n) convergence rate of our prop...
详细信息
This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic O(1/n) convergence rate of our proposed algorithm in non-ergodic sense. Applications of our results to various well-known convex optimization methods, such as the proximal method of multipliers and the alternating direction method of multipliers are given. Numerical results are given to demonstrate the accelerating behaviors of our method over other related methods in the literature. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to b...
详细信息
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case O(1/t) convergence rate, where t denotes the iteration number. By properly choosing the algorithm parameters, numerical experiments on solving a sparse optimization problem arising from statistical learning show that our P-PPA could perform significantly better than other state-of-the-art methods, such as the alternating direction method of multipliers and the relaxed proximal point algorithm.
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomograp...
详细信息
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography, and economics. To solve these generally large-scale LP problems efficiently, we design an implementable inexact entropic proximal point algorithm (iEPPA) combined with an easy-to-implement dual block coordinate descent method as a subsolver. Unlike existing entropy-type proximal point algorithms, our iEPPA employs a more practically checkable stopping condition for solving the associated subproblems while achieving provable convergence. Moreover, when solving the capacity constrained multi-marginal optimal transport (CMOT) problem (a special case of our LP problem), our iEPPA is able to bypass the underlying numerical instability issues that often appear in the popular entropic regularization approach, since our algorithm does not require the proximal parameter to be very small in order to obtain an accurate approximate solution. Numerous numerical experiments show that our iEPPA is efficient and robust for solving some large-scale CMOT problems on synthetic data. The preliminary experiments on the discrete tomography problem also highlight the potential modeling capability of our model.
暂无评论