We study the structure of dual optimization problems associated with linear constraints, bounds on the variables, and separable cost. We show how the separability of the dual cost function is related to the sparsity structure of the linear equations. As a result, techniques for ordering sparse matrices based on nested dissection or graph partitioning can be used to decompose a dual optimization...

The purpose of this study is to develop an effective scheduling methodology for a realistic flow shop sequencing problem. The flow shop consists of two machines where only the first machine has separable, external, and sequence dependent setup times. The length of setup times required for a job depends not on the immediately preceding job but on the job which is two steps prior to it. The probl...

Many real-world optimization models comprise nonconvex and nonlinear as well as nonsmooth functions leading to very hard classes of optimization models. In this article a new interior-point method for the special but practically relevant class of optimization problems with locatable and separable nonsmooth aspects is presented. After motivating and formalizing the problems under consideration, ...

We consider dual coordinate ascent methods for minimizing a strictly convex (possibly nondifferentiable) function subject to linear constraints. Such methods are useful in large-scale applications (e.g., entropy maximization, quadratic programming, network flows), because they are simple, can exploit sparsity and in certain cases are highly parallelizable. We establish their global convergence ...

We study a multiperiod portfolio selection problem in which a single period meanstandard-deviation criterion is used to construct a separable multiperiod selection criterion. Using this criterion, we obtain a closed form optimal strategy which depends on selection schemes of investor’s risk preference. As a consequence, we develop a multiperiod portfolio selection scheme. In doing so, we adapt ...

Abstraet~In this paper, we present a complete decomposition algorithm for nonconvex separable optimization problems applied in the optimal control problems. This complete decomposition algorithm combines recursive quadratic programming with the dual method. When our algorithm is applied to discretized optimal control problems, a simple and parallel computation and a simple and regular data flow...

We present an algorithm for solving nonlinear programming problems involving a partially separable objective function whose derivatives are assumed to be unavailable. At each iteration, we construct a quadratic interpolation model of the objective function around the current iterate and minimize this model to obtain a trial step. The whole process is embedded within a trust-region framework. We...

We consider the fundamental problem of computing an optimal portfolio based on a quadratic mean-variance model of the objective function and a given polyhedral representation of the constraints. The main departure from the classical quadratic programming formulation is the inclusion in the objective function of piecewise linear, separable functions representing the transaction costs. We handle ...

In this paper, we develop a parameterized proximal point algorithm (PPPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case O(1/t) convergence rate, where t denotes the iteration number. By properly choosing the algorithm parameters, numerical experiments on solvin...

We consider low-rank semidefinite programming (LRSDP) relaxations of unconstrained {−1, 1} quadratic problems (or, equivalently, of Max-Cut problems) that can be formulated as the nonconvex nonlinear programming problem of minimizing a quadratic function subject to separable quadratic equality constraints. We prove the equivalence of the LRSDP problem with the unconstrained minimization of a ne...