We propose a direct splitting method for solving nonsmooth variational inequality problems in Hilbert spaces. The weak convergence is established, when the operator is the sum of two point-to-set and monotone operators. The proposed method is a natural extension of the incremental subgradient method for nondifferentiable optimization, which explores strongly the structure of the operator using ...

The problem of establishing minimum-cost multicast connections in coded networks can be viewed as an optimization problem, and decentralized algorithms were proposed by Lun et al. to compute the optimal subgraph using the subgradient method on the dual problem. However, the convergence rate problem for these algorithms remains open. There are limited results in the literature on the convergence...

We study the subgradient projection method for convex optimization with Brr ann-lund's level control for estimating the optimal value. We establish global convergence in objective values without additional assumptions employed in the literature.

When applied to large-scale separable optimization problems, the recently developed surrogate subgradient method for Lagrangian relaxation (Zhao et al.: J. Optim. Theory Appl. 100, 699–712, 1999) does not need to solve optimally all the subproblems to update the multipliers, as the traditional subgradient method requires. Based on it, the penalty surrogate subgradient algorithm was further deve...

In this paper, we consider solution approaches to a multihour combined capacity design and routing problem which arises in the design of dynamically reconfigurable broadband communication networks that uses the virtual path concept. We present a comparative evaluation of four approaches, namely: a genetic algorithm, a Lagrangian relaxation based subgradient optimization method, a generalized pr...

The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to regain feasibility. The latter poses a computational difficulty and, therefore, the projected subgradient method is applicable only when the feasible region ...

In this paper, we consider solution approaches to a multi-hour combined capacity design and routing problem which arises in the design of dynamically reconngurable broadband communication networks that uses the virtual path concept. We present a comparative evaluation of four approaches, namely: a genetic algorithm; a Lagrangean relaxation based subgradient optimization method; a generalized pr...

This paper proposes an optimal algorithm for distributed orbit determination by using discrete observations provided from multiple tracking stations in a connected network. The objective is to increase the precision of estimation by communication and cooperation between tracking stations in the network. We focus on the dynamical approach considering a simplified Low Earth Orbital Satellite mode...

3 Convergence proof 4 3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Some basic inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.3 A bound on the suboptimality bound . . . . . . . . . . . . . . . . . . . . . . 7 3.4 A stopping criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.5 Numerical examp...

In this paper, we study the strong convergence of the Halpern type algorithms for a strongly quasi-nonexpansive sequence of operators. These results extend the results of Saejung [11]. Some applications in infinite family of firmly quasi-nonexpansive mappings, multiparameter proximal point algorithm, constraint minimization and subgradient projection are presented.