arXiv subjects

Rohit Kannan

Publications and source records attributed to Rohit Kannan.

7 recordsLinked to original sources

arXiv2025

Strong Partitioning and a Machine Learning Approximation for Accelerating the Global Optimization of Nonconvex QCQPs

We learn optimal instance-specific heuristics for the global minimization of nonconvex quadratically-constrained quadratic programs (QCQPs). Specifically, we consider partitioning-based convex mixed-integer programming relaxations for nonconvex QCQPs and propose the novel problem of strong partitioning to optimally partition variable domains without sacrificing global optimality. Since solving this max-min strong partitioning problem exactly can be very challenging, we design a local optimization method that leverages generalized gradients of the value function of its inner-minimization problem. However, even solving the strong partitioning problem to local optimality can be time-consuming. To address this, we propose a simple and practical machine learning (ML) approximation for homogeneous families of QCQPs. Motivated by practical applications, we conduct a detailed computational study using the open-source global solver Alpine to evaluate the effectiveness of our ML approximation in accelerating the repeated solution of homogeneous QCQPs with fixed structure. Our study considers randomly generated QCQP families, including instances of the pooling problem, that are benchmarked using state-of-the-art global optimization software. Numerical experiments demonstrate that our ML approximation of strong partitioning reduces Alpine's solution time by a factor of 2 to 4.5 on average, with maximum reduction factors ranging from 10 to 200 across these QCQP families.

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arXiv2025

Bounding-Focused Discretization Methods for the Global Optimization of Nonconvex Semi-Infinite Programs

We use sensitivity analysis to design bounding-focused discretization (cutting-surface) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal bounding-focused discretization of SIPs as a max-min problem and propose variants that are more computationally tractable. We then use parametric sensitivity theory to design an effective heuristic approach for solving these max-min problems. We also show how our new iterative discretization methods may be modified to ensure that the solutions of their discretizations converge to an optimal solution of the SIP. We then formulate optimal bounding-focused generalized discretization of SIPs as max-min problems and design heuristic algorithms for their solution. Numerical experiments on standard nonconvex SIP test instances from the literature demonstrate that our new bounding-focused discretization methods can significantly reduce the number of iterations for convergence relative to a state-of-the-art feasibility-focused discretization method.

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arXiv2022

Data-Driven Sample Average Approximation with Covariate Information

We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of covariates. Given a new covariate observation, the goal is to choose a decision that minimizes the expected cost conditioned on this observation. We investigate three data-driven frameworks that integrate a machine learning prediction model within a stochastic programming sample average approximation (SAA) for approximating the solution to this problem. Two of the SAA frameworks are new and use out-of-sample residuals of leave-one-out prediction models for scenario generation. The frameworks we investigate are flexible and accommodate parametric, nonparametric, and semiparametric regression techniques. We derive conditions on the data generation process, the prediction model, and the stochastic program under which solutions of these data-driven SAAs are consistent and asymptotically optimal, and also derive convergence rates and finite sample guarantees. Computational experiments validate our theoretical results, demonstrate the potential advantages of our data-driven formulations over existing approaches (even when the prediction model is misspecified), and illustrate the benefits of our new data-driven formulations in the limited data regime.

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arXiv2022

Residuals-based distributionally robust optimization with covariate information

We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.

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arXiv2021

Heteroscedasticity-aware residuals-based contextual stochastic optimization

We explore generalizations of some integrated learning and optimization frameworks for data-driven contextual stochastic optimization that can adapt to heteroscedasticity. We identify conditions on the stochastic program, data generation process, and the prediction setup under which these generalizations possess asymptotic and finite sample guarantees for a class of stochastic programs, including two-stage stochastic mixed-integer programs with continuous recourse. We verify that our assumptions hold for popular parametric and nonparametric regression methods.

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arXiv2020

A stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraint violation. To this end, we construct a reformulated problem whose objective is to minimize the probability of constraints violation subject to deterministic convex constraints (which includes a bound on the objective function value). We adapt existing smoothing-based approaches for chance-constrained problems to derive a convergent sequence of smooth approximations of our reformulated problem, and apply a projected stochastic subgradient algorithm to solve it. In contrast with exterior sampling-based approaches (such as sample average approximation) that approximate the original chance-constrained program with one having finite support, our proposal converges to stationary solutions of a smooth approximation of the original problem, thereby avoiding poor local solutions that may be an artefact of a fixed sample. Our proposal also includes a tailored implementation of the smoothing-based approach that chooses key algorithmic parameters based on problem data. Computational results on four test problems from the literature indicate that our proposed approach can efficiently determine good approximations of the efficient frontier.

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arXiv2019

Stochastic DC Optimal Power Flow With Reserve Saturation

We propose an optimization framework for stochastic optimal power flow with uncertain loads and renewable generator capacity. Our model follows previous work in assuming that generator outputs respond to load imbalances according to an affine control policy, but introduces a model of saturation of generator reserves by assuming that when a generator's target level hits its limit, it abandons the affine policy and produces at that limit. This is a particularly interesting feature in models where wind power plants, which have uncertain upper generation limits, are scheduled to provide reserves to balance load fluctuations. The resulting model is a nonsmooth nonconvex two-stage stochastic program, and we use a stochastic approximation method to find stationary solutions to a smooth approximation. Computational results on 6-bus and 118-bus test instances demonstrates that by considering the effects of saturation, our model can yield solutions with lower expected generation costs (at the same target line violation probability level) than those obtained from a model that enforces the affine policy to stay within generator limits with high probability.

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