The hybrid proximal point algorithm introduced by Solodov and Svaiter allowing significant relaxation of the tolerance requirements imposed on the solution of proximal subproblems will be combined with the inertial method introduced by Alvarez and Attouch which incorporates second order information to achieve faster convergence. The weak convergence of the resulting method will be investigated ...

‎the aim of this paper is to study the convergence of solutions of the‎ ‎following second order difference inclusion‎ ‎begin{equation*}begin{cases}exp^{-1}_{u_i}u_{i+1}+theta_i exp^{-1}_{u_i}u_{i-1} in c_ia(u_i),quad igeqslant 1 u_0=xin m‎, ‎quad‎ ‎underset{igeqslant 0}{sup} d(u_i,x)

We introduce and study a new class of nonlinear general A-monotone operator equations with multivalued operator. By using Alber’s inequalities, Nalder’s results, and the new proximal mapping technique, we construct some new perturbed iterative algorithms with mixed errors for solving the nonlinear general A-monotone operator equations and study the approximationsolvability of the nonlinear oper...

We consider a nonhomogeneous first-order evolution equation governed by maximal monotone operator $ A in Hilbert space the presence of Tikhonov regularization term. study existence and strong convergence weak solutions to such systems. With boundedness conditions on central path or solution trajectory, without assuming zero set be nonempty with suitable assumptions coefficient, we prove that sy...

We study the Extended Proximal Auxiliary Problem Principle-method (EPAPP) by Kaplan and Tichatschke [17, 20] for solving variational inequalities whose operator is the sum of a maximal monotone and a continuous operator. As in comparable methods using Bregman distances the authors required that the operator of the considered variational inequality (here called main operator) is paramonotone (se...

We deal with monotone inclusion problems of the form 0 ∈ Ax+Dx+NC(x) in real Hilbert spaces, where A is a maximally monotone operator, D a cocoercive operator and C the nonempty set of zeros of another cocoercive operator. We propose a forwardbackward penalty algorithm for solving this problem which extends the one proposed by H. Attouch, M.-O. Czarnecki and J. Peypouquet in [3]. The condition ...

Based on a common article of the authors, we are concerned with solving monotone inclusion problems expressed by the sum of a set-valued maximally monotone operator with a single-valued maximally monotone one and the normal cone to the nonempty set of zeros of another set-valued maximally monotone operator. Depending on the nature of the single-valued operator, we propose two iterative penalty ...

Abstract This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in optimization algorithms and modeling physical systems. The inclusion described a set-valued mapping having property that, for given time instant, describes maximal monotone operator. By successive application proximal operator, we construct sequence functions parameterize...