We consider the problem of minimization for a function with Lipschitz continuous gradient on a proximally smooth and smooth manifold in a finite dimensional Euclidean space. We consider the Lezanski-Polyak-Lojasiewicz...
详细信息
We consider the problem of minimization for a function with Lipschitz continuous gradient on a proximally smooth and smooth manifold in a finite dimensional Euclidean space. We consider the Lezanski-Polyak-Lojasiewicz (LPL) conditions in this problem of constrained optimization. We prove that the gradient projection algorithm for the problem converges with a linear rate when the LPL condition holds.
In this article, we use the superiorization methodology to investigate the bounded perturbations resilience of the gradient projection algorithm proposed in Erturk et al. (J Nonlinear Convex Anal 21(4):943-951, 2020) ...
详细信息
In this article, we use the superiorization methodology to investigate the bounded perturbations resilience of the gradient projection algorithm proposed in Erturk et al. (J Nonlinear Convex Anal 21(4):943-951, 2020) for solving the convex minimization problem in Hilbert space setting. We obtain that the perturbed version of this gradient projection algorithm converges weakly to a solution of the convex minimization problem just like itself. We support our conclusion with an example in an infinitely dimensional Hilbert space. We also show that the superiorization methodology can be applied to the split feasibility and the inverse linear problems with the help of the perturbed gradient projection algorithm.
A gradient projection algorithm is presented for the dynamic dispatch of thermal generations, based upon an active set strategy and exploiting second order information in determining the descent directions. The algori...
详细信息
A gradient projection algorithm is presented for the dynamic dispatch of thermal generations, based upon an active set strategy and exploiting second order information in determining the descent directions. The algorithm is adapted to the model of the dynamic dispatch problem which consists of the minimisation of a nonlinear objective function subject to quadratic equality constraints and linear inequality constraints. The envisaged algorithm can be applied to the dispatching of thermal units during the steep load pick-up and drop-down periods over short time intervals, and can also be used in the day-before scheduling after the unit commitment has been performed. Efficiency is demonstrated by tests on large-scale networks representative of the Italian EHV system. The limited CPU time requirements also suggest a possible on-line application in determining the constrained participation factors to be used in the Automatic Generation Control function.
gradientprojection (GP) algorithm has been shown as an efficient algorithm for solving the traditional traffic equilibrium problem with additive route costs. Recently, GP has been extended to solve the nonadditive tr...
详细信息
gradientprojection (GP) algorithm has been shown as an efficient algorithm for solving the traditional traffic equilibrium problem with additive route costs. Recently, GP has been extended to solve the nonadditive traffic equilibrium problem (NaTEP), in which the cost incurred on each route is not just a simple sum of the link costs on that route. However, choosing an appropriate stepsize, which is not known a priori, is a critical issue in GP for solving the NaTEP. Inappropriate selection of the stepsize can significantly increase the computational burden, or even deteriorate the convergence. In this paper, a self-adaptive gradientprojection (SAGP) algorithm is proposed. The self-adaptive scheme has the ability to automatically adjust the stepsize according to the information derived from previous iterations. Furthermore, the SAGP algorithm still retains the efficient flow update strategy that only requires a simple projection onto the nonnegative orthant. Numerical results are also provided to illustrate the efficiency and robustness of the proposed algorithm. Published by Elsevier Ltd.
We consider the minimization problem for a nonconvex function with Lipschitz continuous gradient on a proximally smooth (possibly nonconvex) subset of a finite-dimensional Euclidean space. We introduce the error bound...
详细信息
We consider the minimization problem for a nonconvex function with Lipschitz continuous gradient on a proximally smooth (possibly nonconvex) subset of a finite-dimensional Euclidean space. We introduce the error bound condition with exponent alpha is an element of(0, 1] for the gradient mapping. Under this condition, it is shown that the standard gradient projection algorithm converges to a solution of the problem linearly or sublinearly, depending on the value of the exponent alpha. This paper is theoretical. Bibliography: 23 titles.
In this paper, we consider the varying stepsize gradient projection algorithm (GPA) for solving the split equality problem (SEP) in Hilbert spaces, and study its linear convergence. In particular, we introduce a notio...
详细信息
In this paper, we consider the varying stepsize gradient projection algorithm (GPA) for solving the split equality problem (SEP) in Hilbert spaces, and study its linear convergence. In particular, we introduce a notion of bounded linear regularity property for the SEP, and use it to establish the linear convergence property for the varying stepsize GPA. We provide some mild sufficient conditions to ensure the bounded linear regularity property, and then conclude the linear convergence rate of the varying stepsize GPA. To the best of our knowledge, this is the first work to study the linear convergence for the SEP.
This paper presents a new dual formulation for quadratically constrained convex programs. The special structure of the derived dual problem allows us to apply the gradient projection algorithm to produce a simple expl...
详细信息
This paper presents a new dual formulation for quadratically constrained convex programs. The special structure of the derived dual problem allows us to apply the gradient projection algorithm to produce a simple explicit method involving only elementary vector-matrix operations, proven to converge at a linear rate.
In this paper, we study convergence analysis of a new gradient projection algorithm for solving convex minimization problems in Hilbert spaces. We observe that the proposed gradient projection algorithm weakly converg...
详细信息
In this paper, we study convergence analysis of a new gradient projection algorithm for solving convex minimization problems in Hilbert spaces. We observe that the proposed gradient projection algorithm weakly converges to a minimum of convex function f which is defined from a closed and convex subset of a Hilbert space to Double-struck capital R. Also, we give a nontrivial example to illustrate our result in an infinite dimensional Hilbert space. We apply our result to solve the split feasibility problem.
Aiming at the problems of selection parameter step-size and premature convergence that occurred when searching the local area in the optimal design of adaptive gradient projection algorithm in this paper, adaptive var...
详细信息
Aiming at the problems of selection parameter step-size and premature convergence that occurred when searching the local area in the optimal design of adaptive gradient projection algorithm in this paper, adaptive variable step-size mechanism strategy and adaptive variable step-size mechanism were established. They were introduced into the gradient projection algorithm, and were used to control iteration step length. Through the examples of non-probabilistic reliability index, it can be showed that the method could quickly and accurately calculate the reliability index when the model had multiple variables and complex limit state function. To compare and contrast this algorithm with the simple gradient projection algorithm, this algorithm is not sensitive to the initial point position. And it not only takes into account both local performance and global search ability, but also has fast convergence speed and high precision. So it is an efficient and practical optimization algorithm.
In this paper, we propose an incremental gradient projection algorithm for solving a minimization problem over the intersection of a finite family of closed convex subsets of a Hilbert space where the objective functi...
详细信息
In this paper, we propose an incremental gradient projection algorithm for solving a minimization problem over the intersection of a finite family of closed convex subsets of a Hilbert space where the objective function is the sum of component functions. This algorithm is parameterized by a single nonnegative constant i mu. If mu = 0, then the proposed algorithm reduces to the classical incremental gradient method. The weak convergence of the sequence generated by the proposed algorithm is studied if the step size is chosen appropriately. Furthermore, in the special case of constrained least squares problem, the sequence generated by the proposed algorithm is proved to be convergent strongly to a solution of the constrained least squares problem under less requirements for the step size.
暂无评论