Recent advances in nonconvex semi-infinite programming: Applications and algorithms

Djelassi, Hatim; Mitsos, Alexander; Stein, Oliver

doi:10.1016/j.ejco.2021.100006

Cited by 24 publications

(17 citation statements)

References 79 publications

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“…[16] while further details on state‐of‐the‐art numerical methods for GSIPs can be found in, for example, Refs. [9,18,21]. The proper selection of an algorithm for solving () depends on the underlying characteristics of the functions

F = \{f, g_{1}, \dots, g_{m}\}

and the constraint sets

Θ

and

W (θ)

.…”

Section: Problem Formulationmentioning

confidence: 99%

“…It is worth noting that, if Assumption 1 was replaced with standard assumptions from the GSIP literature, then we could directly apply established numerical methods recently summarized in Ref. [9]. However, to the best of our knowledge, no such method exists for functions satisfying Assumption 1, which is the main contribution of this work.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Local and global sensitivity‐based methods 3–5 are often used to study the impact of any critical uncertainties on specific designs; however, such methods focus on robustness analysis amongst a small, finite set of designs, meaning they are unable to systematically synthesize new designs with improved robustness directly. There has been a significant amount of work on so‐called “optimization under uncertainty,” as summarized in several review articles 6–9 . Two main classes of methods for optimization under uncertainty are stochastic and robust optimization.…”

Section: Introductionmentioning

confidence: 99%

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Constrained robust Bayesian optimization of expensive noisy black‐box functions with guaranteed regret bounds

2022

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Many real‐world design problems involve optimization of expensive black‐box functions. Bayesian optimization (BO) is a promising approach for solving such challenging problems using probabilistic surrogate models to systematically tradeoff between exploitation and exploration of the design space. Although BO is often applied to unconstrained problems, it has recently been extended to the constrained setting. Current constrained BO methods, however, cannot identify solutions that are robust to unavoidable uncertainties. In this article, we propose a robust constrained BO method, constrained adversarially robust Bayesian optimization (CARBO), that addresses this challenge by jointly modeling the effect of the design variables and uncertainties on the unknown functions. Using exact penalty functions, we establish a bound on the number of CARBO iterations required to find a near‐global robust solution and provide a rigorous proof of convergence. The advantages of CARBO are demonstrated on two case studies including a non‐convex benchmark problem and a realistic bubble column reactor design problem.

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F = \{f, g_{1}, \dots, g_{m}\}

and the constraint sets

Θ

and

W (θ)

.…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Constrained robust Bayesian optimization of expensive noisy black‐box functions with guaranteed regret bounds

2022

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“…This is the first algorithm that can solve ESIPs to global optimality without any convexity assumptions. Some other recent developments in nonconvex SIP applications and algorithms have been reviewed by Djelassi et al…”

Section: Introductionmentioning

confidence: 99%

Semi-Infinite Optimization with Hybrid Models

Wang

Wilhelm

Stuber

2022

Ind. Eng. Chem. Res.

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The robust design of performance/safety-critical process systems, from a model-based perspective, remains an existing challenge. Hybrid first-principles data-driven models offer the potential to dramatically improve model prediction accuracy, stepping closer to the digital twin concept. Within this context, worst-case engineering design feasibility and reliability problems give rise to a class of semi-infinite program (SIP) formulations with hybrid models as coupling equality constraints. Reduced-space deterministic global optimization methods are exploited to solve this class of SIPs to ϵ-global optimality in finitely many iterations. This approach is demonstrated on two challenging case studies: a nitrification reactor for a wastewater treatment system to address worst-case feasibility verification of dynamical systems and a three-phase separation system plagued by numerical domain violations to demonstrate how they can be overcome using a nonsmooth SIP formulation with hybrid models and a validity constraint incorporated.

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“…Literature review. Despite the difficulty in solving SIP problems for their infinitely many constraints, many algorithms have been proposed in literature [11,19,31]. Most of them consist in generating a sequence of finite problems, with different techniques.…”

Section: Introduction a Semi-infinite Programming (Sip) Problem Is An...mentioning

confidence: 99%

Convergent Algorithms for a Class of Convex Semi-infinite Programs

Cerulli¹,

Oustry²,

d'Ambrosio³

et al. 2022

SIAM J. Optim.

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We focus on convex semi-infinite programs with an infinite number of quadratically parametrized constraints. In our setting, the lower-level problem, i.e., the problem of finding the constraint that is the most violated by a given point, is not necessarily convex. We propose a new convergent approach to solve these semiinfinite programs. Based on the Lagrangian dual of the lower-level problem, we derive a convex and tractable restriction of the considered semi-infinite programming problem. We state sufficient conditions for the optimality of this restriction. If these conditions are not met, the restriction is enlarged through an Inner-Outer Approximation Algorithm, and its value converges to the value of the original semi-infinite problem. This new algorithmic approach is compared with the classical Cutting Plane algorithm. We also propose a new rate of convergence of the Cutting Plane algorithm, directly related to the iteration index, derived when the objective function is strongly convex, and under a strict feasibility assumption. We successfully test the two methods on two applications: the constrained quadratic regression and a zero-sum game with cubic payoff. Our results are compared to those obtained using the approach proposed in [29], as well as using the classical relaxation approach based on the KKT conditions of the lower-level problem.

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Recent advances in nonconvex semi-infinite programming: Applications and algorithms

Cited by 24 publications

References 79 publications

Constrained robust Bayesian optimization of expensive noisy black‐box functions with guaranteed regret bounds

Constrained robust Bayesian optimization of expensive noisy black‐box functions with guaranteed regret bounds

Semi-Infinite Optimization with Hybrid Models

Convergent Algorithms for a Class of Convex Semi-infinite Programs

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