Gradient projection method with a new step size for the split feasibility problem

A Splitting-relaxed Projection Method for Solving the Split Feasibility Problem

The split feasibility problem (SFP) is to find x ∈ C so that Ax ∈ Q, where C is a nonempty closed convex subset of Rn, Q is a nonempty closed convex subset of Rm, and A is a matrix from Rn into Rm. One of successful methods for solving the SFP is Byrne’s CQ algorithm. However, to carry out the CQ algorithm, it is required that the closed convex subsets are simple and that the matrix norm is kno...

An Explicit Method for the Split Feasibility Problem with Self-Adaptive Step Sizes

and Applied Analysis 3 Next we adopt the following notation: i xn → x means that xn converges strongly to x; ii xn ⇀ x means that xn converges weakly to x; iii ωw xn : {x : ∃xnj ⇀ x} is the weak ω-limit set of the sequence {xn}. Recall that a function f : H → R is called convex if f ( λx 1 − λ y ≤ λf x 1 − λ fy, 2.4 for all λ ∈ 0, 1 and ∀x, y ∈ H. It is known that a differentiable function f is...

A Regularized Gradient Projection Method for the Minimization Problem

A Convergent Incremental Gradient Method with a Constant Step Size

Abstract. An incremental gradient method for minimizing a sum of continuously differentiable functions is presented. The method requires a single gradient evaluation per iteration and uses a constant step size. For the case that the gradient is bounded and Lipschitz continuous, we show that the method visits regions in which the gradient is small infinitely often. Under certain unimodality assu...

solution of security constrained unit commitment problem by a new multi-objective optimization method

چکیده-پخش بار بهینه به عنوان یکی از ابزار زیر بنایی برای تحلیل سیستم های قدرت پیچیده ،برای مدت طولانی مورد بررسی قرار گرفته است.پخش بار بهینه توابع هدف یک سیستم قدرت از جمله تابع هزینه سوخت ،آلودگی ،تلفات را بهینه می کند،و هم زمان قیود سیستم قدرت را نیز برآورده می کند.در کلی ترین حالتopf یک مساله بهینه سازی غیر خطی ،غیر محدب،مقیاس بزرگ،و ایستا می باشد که می تواند شامل متغیرهای کنترلی پیوسته و گ...