Related papers: A column generation approach to exact experimental…
Two-stage stochastic unit commitment (2S-SUC) problems have been widely adopted to manage the uncertainties introduced by high penetrations of intermittent renewable energy resources. While decomposition-based algorithms such as…
We apply column generation to approximating complex structured objects via a set of primitive structured objects under either the cross entropy or L2 loss. We use L1 regularization to encourage the use of few structured primitive objects.…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
In this article we introduce Graph Generation, an enhanced Column Generation (CG) algorithm for solving expanded linear programming relaxations of mixed integer linear programs. To apply Graph Generation, we must be able to map any given…
This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class…
We consider optimal experimental design (OED) for Bayesian inverse problems, where the experimental design variables have a certain multiway structure. Given $d$ different experimental variables with $m_i$ choices per design variable $1 \le…
This paper addresses the design of input signals for the purpose of discriminating among a finite set of models dynamic systems within a given finite time interval. A motivating application is fault detection and isolation. We propose…
We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the…
Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
We propose a new pricing strategy for column generation (CG), referred to as Template pricing. This method is motivated by the desire to coordinate solutions of different pricing subproblems in order to accelerate the convergence of the CG…
Optimal designs are required to make efficient statistical experiments. D-optimal designs for some models are calculated by using canonical moments. On the other hand, integrable systems are dynamical systems whose solutions can be written…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
We present a neural network-enhanced column generation (CG) approach for a parallel machine scheduling problem. The proposed approach utilizes an encoder-decoder attention model, namely the transformer and pointer architectures, to develop…
We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators,…
The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width…
The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve…
Stochastic programming provides a natural framework for modeling sequential optimization problems under uncertainty; however, the efficient solution of large-scale multistage stochastic programs remains a challenge, especially in the…