The Convex Hull Heuristic (CHH) is a heuristic for mixed-integer programming problems with a nonlinear objective function and linear constraints. It is a matheuristic in two ways: it is based on the mathematical programming algorithm called simplicial decomposition, or SD, and at each iteration, one solves a mixed-integer programming problem with a linear objective function … Read more
This paper is concerned with a linear control policy for dynamic portfolio selection. We develop this policy by incorporating time-series behaviors of asset returns on the basis of coherent risk minimization. Analyzing the dual form of our optimization model, we demonstrate that the investment performance of linear control policies is directly connected to the intertemporal … Read more
Increasing penetration of wind and renewable generation poses significant challenges to the power system operations and reliability. This paper considers the real-time optimal transmission switching (OTS) problem for determining the generation dispatch and network topology that can account for uncertain energy resources. To efficiently solve the resultant two-stage stochastic program, we propose a tractable linear … Read more
We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a statistician choosing an estimator—that is, a measurable function of the observation—and a fictitious adversary choosing a prior—that is, … Read more
In this paper, we consider the convergence analysis of data-driven mathematical programs with distributionally robust chance constraints (MPDRCC) under weaker conditions without continuity assumption of distributionally robust probability functions. Moreover, combining with the data-driven approximation, we propose a DC approximation method to MPDRCC without some special tractable structures. We also give the convergence analysis of … Read more
In the last years, the gap between solution methods in literature and optimization running in production has increased. Agile development practices, DevOps and modern cloud-based infrastructure call for a revisit of how optimization software is developed. We review the state-of-the-art, propose a development framework that can be applied across different programming languages and modeling frameworks … Read more
In this paper, we solve a class of two-stage distributionally robust optimization problems which have the property of supermodularity. We exploit the explicit upper bounds on the expectation of supermodular functions and derive the worst-case distribution for the robust counterpart. This enables us to develop an efficient method to derive an exact optimal solution of … Read more
The application of mathematical optimization methods provides the capacity to increase the energy efficiency and to lower the investment costs of technical systems, considerably. We present a system approach for the optimization of the design and operation of pumping systems and exemplify it by applying it to the water supply of high-rise buildings. The underlying … Read more
Among many approaches to increase the computational efficiency of semidefinite programming (SDP) relaxation for quadratic constrained quadratic programming problems (QCQPs), exploiting the aggregate sparsity of the data matrices in the SDP by Fukuda et al. (2001) and second-order cone programming (SOCP) relaxation have been popular. In this paper, we exploit the aggregate sparsity of SOCP … Read more
The Nemhauser-Trotter theorem states that the standard linear programming (LP) formulation for the stable set problem has a remarkable property, also known as (weak) persistency: for every optimal LP solution that assigns integer values to some variables, there exists an optimal integer solution in which these variables retain the same values. While the standard LP … Read more