In this paper, the separable programming problem subject to Fuzzy Relation Equation (FRE) constraints is studied. It is decomposed to two subproblems with decreasing and increasing objective functions with the same constraints. They are solved by the maximum solution and one of minimal solutions of its feasible domain, respectively. Their combination produces the original optimal solution. The ...

Today, billions of smart devices are interconnected via wireless networks, leading to large volumes video contents circulating through the bandwidth-limited backhaul. This causes network performance deteriorate. As a mitigation mechanism, caching highly popular edges is deployed. We propose cooperative and demand-aware strategy, which modelled using Separable Assignment Problem, maximize cache ...

The classical alternating direction method (ADM) has been well studied in the context of linearly constrained convex programming problems and variational inequalities where both the involved operators and constraints are separable into two parts. In particular, recentness has witnessed a number of novel applications arising in diversified areas (e.g. Image Processing and Statistics), for which ...

1. Abstract An approach to multiobjective optimization is to define a scalar substitute objective function that aggregates all objectives and solve the resulting aggregate optimization problem (AOP). In this paper, we discern that the objective function in quasi-separable multidisciplinary design optimization (MDO) problems can be viewed as such an aggregate objective function (AOF). We consequ...

We consider a general class of dynamic programming (DP) problems with nonseparable objective functions. show that for any problem in this class, there exists an augmented-state DP satisfies the principle optimality and solutions to which yield original problem. Furthermore, we identify subclass naturally forward separable functions state-augmentation scheme is tractable. extend framework stocha...

The alternating direction method (ADM) is classical for solving a linearly constrained separable convex programming problem (primal problem), and it is well known that ADM is essentially the application of a concrete form of the proximal point algorithm (PPA) (more precisely, the Douglas-Rachford splitting method) to the corresponding dual problem. This paper shows that an efficient method comp...

n-Fold integer programming is a fundamental problem with a variety of natural applications in operations research and statistics. Moreover, it is universal and provides a new, variable-dimension, parametrization of all of integer programming. The fastest algorithm for n-fold integer programming predating the present article runs in time O ( ng(A)L ) with L the binary length of the numerical par...

The multi-level programming problem is defined as an n-person nonzero-sum game with perfect information in which the players move sequentially. The bi-level linear case is addressed in detail. Solutions are obtained by recasting this problem as a standard mathematical probram and appealing to its implicitly separable structure. The reformulated optimization problem is linear save for a ~ompleme...