A Smoothing Function Approach to Joint Chance-Constrained Programs

Shan, Feng; Zhang, Liwei; Xiao, Xiantao

doi:10.1007/s10957-013-0513-3

Cited by 23 publications

(19 citation statements)

References 14 publications

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“…In terms of numerical solution methods for solving CCPs, most approaches have aimed at computing a global minimizer, at least in some sense. For example, when the CCP itself is convex, one can apply standard convex optimization techniques to find a global minimizer [11,13,26,43,44]. On the other hand, if the CCP is not convex, then one may instead be satisfied by finding a global minimizer of an approximate problem constructed so that the feasible region of the chance constraint is convex [9,15,38,40,41].…”

mentioning

confidence: 99%

A Sequential Algorithm for Solving Nonlinear Optimization Problems with Chance Constraints

Curtis¹,

Wächter²,

Zavala³

2018

SIAM J. Optim.

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An algorithm is presented for solving nonlinear optimization problems with chance constraints, i.e., those in which a constraint involving an uncertain parameter must be satisfied with at least a minimum probability. In particular, the algorithm is designed to solve cardinality-constrained nonlinear optimization problems that arise in sample average approximations of chance-constrained problems, as well as in other applications in which it is only desired to enforce a minimum number of constraints. The algorithm employs a novel penalty function, which is minimized sequentially by solving quadratic optimization subproblems with linear cardinality constraints. Properties of minimizers of the penalty function in relation to minimizers of the corresponding nonlinear optimization problem are presented, and convergence of the proposed algorithm to a stationary point of the penalty function is proved. The effectiveness of the algorithm is demonstrated through numerical experiments with a nonlinear cash flow problem.

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mentioning

confidence: 99%

A Sequential Algorithm for Solving Nonlinear Optimization Problems with Chance Constraints

Curtis¹,

Wächter²,

Zavala³

2018

SIAM J. Optim.

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“…In this section we investigate the performance of the algorithm on nonlinear example that appeared in the numerical sections of the state-of-the-art methods in [30] and [31]. Both of these methods are scenarios (or sample) based and use the indicator function approximation (although they approach it in different ways).…”

Section: Nonlinear Joint Chance Constrained Examplementioning

confidence: 99%

“…Both of these methods are scenarios (or sample) based and use the indicator function approximation (although they approach it in different ways). In the method described in [30], the constraints need to be convex in x and the problem can be a joint chance constrained one. In the method described in [31], the constraints do not have to be convex, but must be continuously differentiable in x and the authors deal with a single chance constraint only.…”

Section: Nonlinear Joint Chance Constrained Examplementioning

confidence: 99%

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Pool & Discard Algorithm for Chance Constrained Optimization Problems

Kůdela

Popela

2020

IEEE Access

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In this paper, we describe an effective algorithm for handling chance constrained optimization problems, called the Pool & Discard algorithm. The algorithm utilizes the scenario approximation framework for chance constrained optimization problems, and the warm-start and problem modification features of modern solvers. The exploitation of the problem structure and efficient implementation allows us to considerably speed up the computations, especially for large instances, when compared with conventional methods. INDEX TERMS Chance constrained programming, scenario approximation, P&D algorithm, stochastic programming, constraint removal.

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“…The left hand side of the above inequality is well known as conditional value at risk (CVaR), i.e., From Figure 1 we can see that, although CVaR approximation is the best convex conservative approximation, it is not a good approximation. In [10,23,19], the DC approximation is applied by using…”

Section: Jian Gu Xiantao Xiao and Liwei Zhangmentioning

confidence: 99%

A subgradient-based convex approximations method for DC programming and its applications

Gu¹,

Xiao²,

Zhang³

2016

JIMO

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We consider an optimization problem that minimizes a function of the form f = f 0 + f 1 − f 2 with the constraint g − h ≤ 0, where f 0 is continuous differentiable, f 1 , f 2 are convex and g, h are lower semicontinuous convex. We propose to solve the problem by an inexact subgradient-based convex approximations method. Under mild assumptions, we show that the method is guaranteed to converge to a stationary point. Finally, some preliminary numerical results are given.

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A Smoothing Function Approach to Joint Chance-Constrained Programs

Cited by 23 publications

References 14 publications

A Sequential Algorithm for Solving Nonlinear Optimization Problems with Chance Constraints

A Sequential Algorithm for Solving Nonlinear Optimization Problems with Chance Constraints

Pool & Discard Algorithm for Chance Constrained Optimization Problems

A subgradient-based convex approximations method for DC programming and its applications

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