A new exact penalty method for semi-infinite programming problems

Lin, Qun; Loxton, Ryan; Teo, Kok Lay; Wu, Yong; Yu, Changjun

doi:10.1016/j.cam.2013.11.010

Cited by 56 publications

(61 citation statements)

References 16 publications

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“…Thus, Problem B cannot be solved directly by MISER 3.3, which requires the objective to be smooth. In the next subsection, we overcome this difficulty by introducing new binary variables (adopting the transformation strategy described in [8,19]) in addition to new linear and quadratic constraints.…”

Section: Application Of the Time-scaling Techniquementioning

confidence: 99%

“…In the next section, we apply the exact penalty method proposed in [8] to transform Problem C into an unconstrained problem, which can then be solved readily by MISER 3.3.…”

Section: • the Jump Conditions (19)-(20);mentioning

confidence: 99%

“…We now formulate an optimal control problem as follows: Choose the harvesting fractions ν j and the corresponding harvesting times τ j to maximize the revenue function defined by (8) and (9a) subject to the dynamics described by equations (10) and (11), the constraints given by (3) and (4) and the jump conditions given by (5) and (6). We refer to this problem as Problem A.…”

Section: Is the Sale Price Of Shrimp In Dollars Per Kilogram (As A Fumentioning

confidence: 99%

“…The penalty terms are zero at feasible points and positive at infeasible points. Prior research [8,19,20] indicates that any local minimizer of the unconstrained problem will be a local minimizer of the original problem when the penalty parameter is sufficiently large.…”

Section: Introductionmentioning

confidence: 99%

“…Although the time-scaling transformation eliminates the variability in the jump times, it does not eliminate the discontinuity in the objective function. Hence, inspired by the relaxation approaches in [8,12,20], we introduce new binary variables into the objective function, together with linear and quadratic constraints, to transform the objective function into a smooth function. The resulting optimization problem can be solved using an exact penalty method.…”

Section: Introductionmentioning

confidence: 99%

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A computational algorithm for a class of non-smooth optimal control problems arising in aquaculture operations

Blanchard

Loxton

Rehbock

2013

Applied Mathematics and Computation

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This paper introduces a computational approach for solving non-linear optimal control problems in which the objective function is a discontinuous function of the state. We illustrate this approach using a dynamic model of shrimp farming in which shrimp are harvested at several intermediate times during the production cycle. The problem is to choose the optimal harvesting times and corresponding optimal harvesting fractions (the percentage of shrimp stock extracted) to maximize total revenue. The main difficulty with this problem is that the selling price of shrimp is modelled as a piecewise constant function of the average shrimp weight and thus the revenue function is discontinuous. By performing a time-scaling transformation and introducing a set of auxiliary binary variables, we convert the shrimp harvesting problem into an equivalent optimization problem that has a smooth objective function. We then use an exact penalty method to solve this equivalent problem. We conclude the paper with a numerical example.

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Section: Application Of the Time-scaling Techniquementioning

confidence: 99%

“…In the next section, we apply the exact penalty method proposed in [8] to transform Problem C into an unconstrained problem, which can then be solved readily by MISER 3.3.…”

Section: • the Jump Conditions (19)-(20);mentioning

confidence: 99%

Section: Is the Sale Price Of Shrimp In Dollars Per Kilogram (As A Fumentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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