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Existing techniques for the cost optimization of water distribution networks either employ meta-heuristics, or try to develop problem-specific optimization techniques. Instead, we exploit recent advances in generic NLP solvers and explore a…
The nonlinear, non-convex AC Optimal Power Flow (AC-OPF) problem is fundamental for power systems operations. The intrinsic complexity of AC-OPF has fueled a growing interest in the development of optimization proxies for the problem, i.e.,…
We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem $\min_{\mathbf{x} \in \mathbf{S}}\{ (f_1(\mathbf{x}), f_2(\mathbf{x})) \}$, where $f_1$ and $f_2$ are two…
Partitioning for load balancing is a crucial first step to parallelize any type of computation. In this work, we propose SGORP, a new spatial partitioning method based on Subgradient Optimization, to solve the $d$-dimensional Rectilinear…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…
We investigate relaxations for a class of discrete bilevel programs where the interaction constraints linking the leader and the follower are linear. Our approach reformulates the upper-level optimality constraints by projecting the…
In this paper, we discuss our approach and algorithmic framework for solving large-scale security constrained optimal power flow (SCOPF) problems. SCOPF is a mixed integer non-convex optimization problem that aims to obtain the minimum…
This paper provides a classification of real scheduling problems. Various ways have been examined and described on the problem. Scheduling problem faces a tremendous challenges and difficulties in order to meet the preferences of the…
Randomized rounding is a technique that was originally used to approximate hard offline discrete optimization problems from a mathematical programming relaxation. Since then it has also been used to approximately solve sequential stochastic…
We present a decomposition approach for obtaining good feasible solutions for the security-constrained alternating-current optimal power flow (SCACOPF) problem at an industrial scale and under real-world time and computational limits. The…
We present a set of integer programs (IPs) for the Steiner tree problem with the property that the best solution obtained by solving all, provides an optimal Steiner tree. Each IP is polynomial in the size of the underlying graph and our…
Fluid models provide a tractable approach to approximate multiclass processing networks. This tractability is a due to the fact that optimal control for such models is a solution of a Separated Continuous Linear Programming (SCLP) problem.…
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
This paper considers how to fuse Machine Learning (ML) and optimization to solve large-scale Supply Chain Planning (SCP) optimization problems. These problems can be formulated as MIP models which feature both integer (non-binary) and…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of…
We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result such…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…
We consider single-machine scheduling problems that are natural generalizations or variations of the min-sum set cover problem and the min-sum vertex cover problem. For each of these problems, we give new approximation algorithms. Some of…