335 research outputs found
On Convergence Analysis of Gradient Based Primal-Dual Method of Multipliers
© 2018 IEEE. Recently, the primal-dual method of multipliers (PDMM) has been proposed and successfully applied to solve a number of decomposable convex optimizations distributedly and iteratively. In this work, we study the gradient based PDMM (GPDMM), where the objective functions are approximated using the gradient information per iteration. It is shown that for a certain class of decomposable convex optimizations, synchronous GPDMM has a sublinear convergence rate of O(1/K) (where K denotes the iteration index). Experiments on a problem of distributed ridge regularized logistic regression demonstrate the efficiency of synchronous GPDMM
Network Target Coordination for Design Optimization of Decomposed Systems
A complex engineered system is often decomposed into a number of different subsystems that interact on one another and together produce results not obtainable by the subsystems alone. Effective coordination of the interdependencies shared among these subsystems is critical to fulfill the stakeholder expectations and technical requirements of the original system. The past research has shown that various coordination methods obtain different solution accuracies and exhibit different computational efficiencies when solving a decomposed system. Addressing these coordination decisions may lead to improved complex system design. This dissertation studies coordination methods through two types of decomposition structures, hierarchical, and nonhierarchical. For coordinating hierarchically decomposed systems, linear and proximal cutting plane methods are applied based on augmented Lagrangian relaxation and analytical target cascading (ATC). Three nonconvex, nonlinear design problems are used to verify the numerical performance of the proposed coordination method and the obtained results are compared to traditional update schemes of subgradient-based algorithm. The results suggest that the cutting plane methods can significantly improve the solution accuracy and computational efficiency of the hierarchically decomposed systems. In addition, a biobjective optimization method is also used to capture optimality and feasibility. The numerical performance of the biobjective algorithm is verified by solving an analytical mass allocation problem. For coordinating nonhierarchically decomposed complex systems, network target coordination (NTC) is developed by modeling the distributed subsystems as different agents in a network. To realize parallel computing of the subsystems, NTC via a consensus alternating direction method of multipliers is applied to eliminate the use of the master problem, which is required by most distributed coordination methods. In NTC, the consensus is computed using a locally update scheme, providing the potential to realize an asynchronous solution process. The numerical performance of NTC is verified using a geometrical programming problem and two engineering problems
A decomposition algorithm for two-stage stochastic programs with nonconvex recourse
In this paper, we have studied a decomposition method for solving a class of
nonconvex two-stage stochastic programs, where both the objective and
constraints of the second-stage problem are nonlinearly parameterized by the
first-stage variable. Due to the failure of the Clarke regularity of the
resulting nonconvex recourse function, classical decomposition approaches such
as Benders decomposition and (augmented) Lagrangian-based algorithms cannot be
directly generalized to solve such models. By exploring an implicitly
convex-concave structure of the recourse function, we introduce a novel
decomposition framework based on the so-called partial Moreau envelope. The
algorithm successively generates strongly convex quadratic approximations of
the recourse function based on the solutions of the second-stage convex
subproblems and adds them to the first-stage master problem. Convergence under
both fixed scenarios and interior samplings is established. Numerical
experiments are conducted to demonstrate the effectiveness of the proposed
algorithm
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