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We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
Reformulating nonlinear optimization problems into solver-ready linear optimization problems is often necessary for practical applications, but the process is often manual and requires domain expertise. We propose LinearizeLLM, an…
In this paper, we propose a new mixed-integer linear programming (MILP) model ontology and a novel constraint typology of MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life…
In this study, we introduce an innovative deep learning framework that employs a transformer model to address the challenges of mixed-integer programs, specifically focusing on the Capacitated Lot Sizing Problem (CLSP). Our approach, to our…
This chapter presents reduced-rank linearly constrained minimum variance (LCMV) algorithms based on the concept of joint iterative optimization of parameters. The proposed reduced-rank scheme is based on a constrained robust joint iterative…
Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…
In this paper, an algorithm is developed to solve a multilevel mono-objective linear programming problem (ML(MO)LPP), where the constructive adaptive method of linear programming is nested. This procedure is the modified version of the SB.…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…
We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of…
The fully connected conditional random field (CRF) with Gaussian pairwise potentials has proven popular and effective for multi-class semantic segmentation. While the energy of a dense CRF can be minimized accurately using a linear…
We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding…
Powerful interior-point methods (IPM) based commercial solvers, such as Gurobi and Mosek, have been hugely successful in solving large-scale linear programming (LP) problems. The high efficiency of these solvers depends critically on the…
Designing trajectories for manipulation through contact is challenging as it requires reasoning of object \& robot trajectories as well as complex contact sequences simultaneously. In this paper, we present a novel framework for…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and…
An integer program is called ideal if its continuous relaxation coincides with its convex hull allowing the problem to be solved as a continuous program and offering substantial computational advantages. Proving idealness analytically can…
The rolling stock rotation problem with predictive maintenance (RSRP-PdM) involves the assignment of trips to a fleet of vehicles with integrated maintenance scheduling based on the predicted failure probability of the vehicles. These…