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The main purpose of this paper is to introduce a viscosity-type proximal point algorithm for approximating a common solution of a finite family of equilibrium problems and fixed point problem for a certain class of nonspreading-type mappings recently introduced by Phuengrattana [Applied General Topology 18(2017), 117-129]. We further establish a strong convergence of our proposed algorithm to a common solution of a finite family of equilibrium problems which is also a fixed point of this class of mappings and a unique solution of some variational inequality problems in an Hadamard space. We also analyse the asymptotic behaviour of the sequence generated by a viscosity-type algorithm and extend the analysis to approximate a common solution of a finite family of equilibrium problems in an Hadamard space. Furthermore, we applied our results to solve some optimization problems in Hadamard spaces. [ABSTRACT FROM AUTHOR]

In this paper we propose the forward–backward splitting methods with linesearches for solving nonsmooth optimization problems without the standard assumption of the Lipschitz continuity of the gradient in Banach spaces. We prove the weak convergence of the iterative sequence generated by these methods, and further prove convergence with asymptotic rate 1 n to the optimal value under the assumption of the boundedness of the iterative sequence. [ABSTRACT FROM AUTHOR]

In this paper, we first give two versions of the Fenchel duality formula and Brøndsted-Rockafellar's theorem. The versions are useful and the proofs are not so difficult. Next, we present a theorem in a Banach space to reconsider the Ekeland variational principle and Takahashi's nonconvex minimization theorem proved in a complete metric space. Finally, using the version of the Fenchel duality formula, the Ekeland variational principle and the version of Brøndsted-Rockafellar's theorem, we prove a minimization theorem in a Banach space and then present a short proof of well–known Rockafellar's theorem for maximal monotonicity of subdifferentials. [ABSTRACT FROM AUTHOR]

Let X be a uniformly smooth and 2-uniformly convex real Banach space with dual space X ∗ . In this paper, a Halpern-type subgradient extragradient algorithm is constructed. The sequence, generated by the algorithm, converges strongly to a common solution of variational inequality and two convex minimization problems. This result is obtained as an application of a Halpern-type subgradient extragradient algorithm, for approximating a common solution of variational inequality and J-fixed points of two continuous J-pseudocontractions. The theorem proved complements, improves and unifies many recent results in the literature. Finally, numerical experiments are given to illustrate the convergence of the sequence generated by the algorithm. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces.

This paper presents a fast and robust algorithm for contact detection between elliptical and ellipsoidal particles. The algorithm belongs to the class of geometrical potential methods, which consider the solution of two minimization problems in order to determine a contact point between the particles. The efficiency of the algorithm relies on several ingredients, namely, a transformation that maps the pair of ellipses (ellipsoids) into an ellipse (ellipsoid) centered at the origin and a unit circle (sphere), the construction of an effective initial guess to the solution of the minimization problem, the use of Newton's method for the root finding problem, and the introduction of an additional constraint to guarantee convergence to the desired root. The performance of the new algorithm is compared with that of existing contact detection algorithms on large sets of randomly generated pairs of particles. In particular, the results from several numerical examples show that the present algorithm is several times faster than the existing algorithms for comparable accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we have discussed and investigated two nonlinear extended PR-CG method which use function and gradient values. The two new methods involve the standard CG-methods and have the sufficient descent and globally convergence properties under certain conditions. We have got some important numerical results by comparing the new method with Wu and Chen PRCG-(2010) method in this field.

The main purpose of this paper is to introduce some viscosity-type proximal point algorithms which comprise of a nonexpansive mapping and a finite sum of resolvents of monotone operators, and prove their strong convergence to a common zero of a finite family of monotone operators which is also a fixed point of a nonexpansive mapping and a unique solution of some variational inequality problems in an Hadamard space. We apply our results to solve a finite family of convex minimization problems, variational inequality problems and convex feasibility problems. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we propose the modified splitting method for accretive operators in Banach space and prove some strong convergence theorems of the proposed method under suitable conditions. Our main results can be viewed as the improvement of the results of Takahashi et al. Indeed, we remove the conditions that limn→∞(rn−rn+1)=0 in our results. Moreover, we extend their results in Hilbert spaces to certain Banach spaces. Finally, we give some applications to the minimization problems with convergence analysis. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce iterative algorithm solving split system of minimization problem given as a task of finding a common minimizer point of finite family of proper, lower semicontinuous convex functions and whose image under a bounded linear operator is also common minimizer point of another finite family of proper, lower semicontinuous convex functions. We obtain strong convergence of the sequence generated by our algorithm under some suitable conditions on the parameters. The iterative schemes are developed with a way of selecting the step sizes such that the information of operator norm is not necessary. Some applications and numerical experiment is given to analyse the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

Purpose: Patients who have medical metallic implants, e.g. orthopaedic implants and pacemakers, often cannot undergo an MRI exam. One of the largest risks is tissue heating due to the radio frequency (RF) fields. The RF safety assessment of implants is computationally demanding. This is due to the large dimensions of the transmit coil compared to the very detailed geometry of an implant. Methods: In this work, we explore a faster computational method for the RF safety assessment of implants that exploits the small geometry. The method requires the RF field without an implant as a basis and calculates the perturbation that the implant induces. The inputs for this method are the incident fields and a library matrix that contains the RF field response of every edge an implant can occupy. Through a low‐rank inverse update, using the Sherman–Woodbury–Morrison matrix identity, the EM response of arbitrary implants can be computed within seconds. We compare the solution from full‐wave simulations with the results from the presented method, for two implant geometries. Results: From the comparison, we found that the resulting electric and magnetic fields are numerically equivalent (maximum error of 1.35%). However, the computation was between 171 to 2478 times faster than the corresponding GPU accelerated full‐wave simulation. Conclusions: The presented method enables for rapid and efficient evaluation of the RF fields near implants and might enable situation‐specific scanning conditions. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces. [ABSTRACT FROM AUTHOR]

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In this paper, we introduce certain regularizations for bifunctions, based on the corresponding regularization for functions, originally defined by J-P. Crouzeix. We show that the equilibrium problems associated to a bifunction and its regularizations are equivalent in the sense that they share the same solution set. Also, we introduce new existence results for the Equilibrium Problem, and we show some applications to minimization and Nash equilibrium problems. [ABSTRACT FROM AUTHOR]

In this paper, we have discussed and investigated two nonlinear extended PR-CG method which use function and gradient values. The two new methods involve the standard CG-methods and have the sufficient descent and globally convergence properties under certain conditions. We have got some important numerical results by comparing the new method with Wu and Chen PRCG-(2010) method in this field.

We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained via concentration compactness. [ABSTRACT FROM AUTHOR]

In this paper we review recent results on the existence of non-topological solitons in classical relativistic nonlinear field theories. We follow the Coleman approach, which is based on the existence of two conservation laws, energy and charge. In particular we show that under mild assumptions on the nonlinear term it is possible to prove the existence of solitons for a set of admissible charges. This set has been studied for the nonlinear Klein–Gordon equation, and in this paper we state new results in this direction for the Klein–Gordon–Maxwell system.

Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) W-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations. [ABSTRACT FROM AUTHOR]

By virtue of numerical arguments we study a bifurcation phenomenon occurring for a class of minimization problems associated with the so-called quasi-linear Schrödinger equation, object of various investigations in the last two decades. [ABSTRACT FROM AUTHOR]

We show that the variational limit of a ℇ-soft and thin junction problem (𝒫ℇ) with sources concentrated in the junction gives rise to a surface energy mixing the internal energy and sources. The surface energy functional possesses an integral representation with respect to the gradient Young-concentration measures generated by sequences (ūℇ)ℇ>0 of minimizers of (𝒫ℇ). [ABSTRACT FROM AUTHOR]

We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order 1/√ϵ concentrated on an e-neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of these measures. [ABSTRACT FROM AUTHOR]

As a rule, the quadratic functional depending on a great number of binary variables has a lot of local minima. One of approaches allowing to find (in averaged) deeper local minima is aggregation of binary variables into larger blocks/domains. To minimize the functional one has to change the states of aggregated variables (domains). In present publication we discuss methods of domains formation. It is shown that the best results are obtained when domains are formed by variables that are strongly connected with each other. [ABSTRACT FROM AUTHOR]

In this paper we study the connection between the metric projection operator P K : B → K, where B is a reflexive Banach space with dual space B* and K is a non–empty closed convex subset of B, and the generalized projection operators ∏ K : B → K and π K : B* → K. We also present some results in non–reflexive Banach spaces. [ABSTRACT FROM AUTHOR]