The alternating direction method of multipliers (ADMM) is being widely used for various convex programming models with separable structures arising in specifically many scientific computing areas. The ADMM’s worst-case O(1/n) convergence rate measured by the iteration complexity has been established in the literature when its penalty parameter is a constant, where n is the iteration … Read more
The cooperative energy management of aggregated buildings has recently received a great deal of interest due to substantial potential energy savings. These gains are mainly obtained in two ways: (i) Exploiting the load shifting capabilities of the cooperative buildings; (ii) Utilizing the expensive but energy efficient equipment that is commonly shared by the building community … Read more
Physical properties of materials are seldom studied in the context of packing problems. In this work we study the behavior of semifluids: materials with particular characteristics, that share properties both with solids and with fluids. We describe the importance of some specific semifluids in an industrial context, and propose methods for tackling the problem of … Read more
Nonlinear disjunctive convex sets arise naturally in the formulation or solution methods of many discrete–continuous optimization problems. Often, a tight algebraic representation of the disjunctive convex set is sought, with the tightest such representation involving the characterization of the convex hull of the disjunctive convex set. In the most general case, this can be explicitly … Read more
We provide Frank-Wolfe ($\equiv$ Conditional Gradients) method with a convergence analysis allowing to approach a primal-dual solution of convex optimization problem with composite objective function. Additional properties of complementary part of the objective (strong convexity) significantly accelerate the scheme. We also justify a new variant of this method, which can be seen as a trust-region … Read more
We propose a decomposition based method for solving mixed-integer nonlinear optimization problems with “black-box” nonlinearities, where the latter, e.g., may arise due to differential equations or expensive simulation runs. The method alternatingly solves a mixed-integer linear master problem and a separation problem for iteratively refining the mixed-integer linear relaxation of the nonlinearity. We prove that … Read more
We present a MATLAB implementation of the shape-changing sym- metric rank-one (SC-SR1) method that solves trust-region subproblems when a limited-memory symmetric rank-one (L-SR1) matrix is used in place of the true Hessian matrix. The method takes advantage of two shape-changing norms [4, 3] to decompose the trust-region subproblem into two separate problems. Using one of … Read more
Risk-averse mixed-integer multi-stage stochastic programming forms a class of extremely challenging problems since the problem size grows exponentially with the number of stages, the problem is non-convex due to integrality restrictions and the objective function is a dynamic measure of risk. For this reason, we propose a scenario tree decomposition approach, namely group subproblem approach, … Read more
We consider the 0-1 Knapsack Problem with Setups (KPS). Items are grouped into families and if any items of a family are packed, this induces a setup cost as well as a setup resource consumption. We introduce a new dynamic programming algorithm which performs much better than a previous dynamic program and turns out to … Read more
This paper presents an extended version of the separation plane algorithms for subgradient-based finite-dimensional nondifferentiable convex blackbox optimization. The extension introduces additional cuts for epigraph of the conjugate of objective function which improve the convergence of the algorithm. The case of affine cuts is considered in more details and it is shown that it requires … Read more