Applications – Science and Engineering – Page 11

Quadratic Optimization Models for Balancing Preferential Access and Fairness: Formulations and Optimality Conditions

Published: 2021/11/04, Updated: 2024/02/19

Applications - Science and Engineering, Convex and Nonsmooth Optimization facilities planning and design, fairness, KKT optimality conditions, resource allocation, Waste management

Typically, within facility location problems, fairness is defined in terms of accessibility of users. However, for facilities perceived as undesirable by communities hosting them, fairness between the usage of facilities becomes especially important. Limited research exists on this notion of fairness. To close this gap, we develop a series of optimization models for the allocation … Read more

A Graph-based Decomposition Method for Convex Quadratic Optimization with Indicators

Published: 2021/10/21

(Mixed) Integer Nonlinear Programming, Statistics convex hull, decomposition, Fenchel dual, graphical models, indicator variables, Quadratic optimization, sparsity

In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix Q defining the quadratic term in the objective is sparse. We use a graphical representation of the support of Q, and show that if this graph is a path, then we can solve the associated problem in polynomial time. This … Read more

ADMM-based Unit and Time Decomposition for Price Arbitrage by Cooperative Price-Maker Electricity Storage Units

Published: 2021/10/21

Miguel F. Anjos

James Cruise

Albert Solà Vilalta

Convex Optimization, Dynamic Programming, Energy admm, control, cooperative problem, energy, horizons, multiple storage units, price arbitrage, price-maker

Decarbonization via the integration of renewables poses significant challenges for electric power systems, but also creates new market opportunities. Electric energy storage can take advantage of these opportunities while providing flexibility to power systems that can help address these challenges. We propose a solution method for the optimal control of multiple price-maker electric energy storage … Read more

Contextual Decision-making under Parametric Uncertainty and Data-driven Optimistic Optimization

Published: 2021/10/14, Updated: 2021/10/15

Junyu Cao

Rui Gao

Robust Optimization, Statistics, Stochastic Programming contextual optimization; joint learning and optimization; data-driven optimization; robust optimization; optimism principle

We consider decision-making problems with contextual information, in which the reward function involves uncertain parameters that can be predicted using covariates. To quantify the uncertainty of the reward, we propose a new parameter uncertainty set based on a supervised learning oracle. We show that the worst/best-case reward over the proposed parameter uncertainty set serves as … Read more

An Improved Penalty Algorithm using Model Order Reduction for MIPDECO problems with partial observations

Published: 2021/10/09

(Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs exact penalty methods, interior point methods, mixed integer optimization, model order reduction, pde-constrained optimization

This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The resulting problem poses several numerical challenges due to the mixture of combinatorial aspects, induced by integer variables, and large scale linear algebra … Read more

Data-Driven Ranges of Near-Optimal Actions for Finite Markov Decision Processes

Published: 2021/10/05

Applications - OR and Management Sciences, Applications - Science and Engineering, Dynamic Programming cardiovascular diseases, health policy, markov decision processes, medical decision making, simulation, statistical multiple comparisons

Markov decision process (MDP) models have been used to obtain non-stationary optimal decision rules in various applications, such as treatment planning in medical decision making. However, in practice, decision makers may prefer other strategies that are not statistically different from the optimal decision rules. To benefit from the decision makers’ expertise and provide flexibility in … Read more

Inexact bilevel stochastic gradient methods for constrained and unconstrained lower-level problems

Published: 2021/10/01, Updated: 2022/12/07

Tommaso Giovannelli

Griffin D. Kent

Luis Nunes Vicente

Data-Mining, Nonlinear Optimization, Stochastic Programming bilevel optimization, DARTS, machine learning, stochastic gradient descent

Two-level stochastic optimization formulations have become instrumental in a number ofmachine learning contexts such as continual learning, neural architecture search, adversariallearning, and hyperparameter tuning. Practical stochastic bilevel optimization problemsbecome challenging in optimization or learning scenarios where the number of variables ishigh or there are constraints. In this paper, we introduce a bilevel stochastic gradient method … Read more

Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach

Published: 2021/09/30, Updated: 2023/11/13

Dimitris Bertsimas

Ryan Cory-Wright

Nicholas A. G. Johnson

Applications - OR and Management Sciences, Data-Mining, Statistics Branch-and-Bound, convex relaxation, matrix decomposition, rank, sparsity

We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental problem in Operations Research and Machine Learning which arises in various applications, including data compression, latent semantic indexing, … Read more

Comparing Solution Paths of Sparse Quadratic Minimization with a Stieltjes Matrix

Published: 2021/09/29

Nonsmooth Optimization, Quadratic Programming, Statistics solution paths, sparse optimization, strong polynomiality, surrogate sparsity functions

This paper studies several solution paths of sparse quadratic minimization problems as a function of the weighing parameter of the bi-objective of estimation loss versus solution sparsity. Three such paths are considered: the “L0-path” where the discontinuous L0-function provides the exact sparsity count; the “L1-path” where the L1-function provides a convex surrogate of sparsity count; … Read more

Approximate Dynamic Programming for Crowd-shipping with In-store Customers

Published: 2021/09/27, Updated: 2021/11/18

Civil and Environmental Engineering, Dynamic Programming, Transportation approximate dynamic programming, crowd-shipping, last-mile delivery, markov decision processes, value function approximation

Crowd-shipping has gained significant attention as a last-mile delivery option over the recent years. In this study, we propose a variant of dynamic crowd-shipping model with in-store customers as crowd-shippers to deliver online orders within few hours. We formulate the problem as a Markov decision process and develop an approximate dynamic programming (ADP) policy using … Read more