Bounded-error optimal experimental design via global solution of constrained min–max program

Walz, Olga; Djelassi, Hatim; Caspari, Adrian; Mitsos, Alexander

doi:10.1016/j.compchemeng.2017.12.016

Cited by 16 publications

(13 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The GSIP algorithm in Reference requires continuity of all functions and equations and the existence of a Slater point arbitrarily close to a GSIP optimum in the objective. As shown in Reference the assumption of an ε ‐optimal GSIP Slater point is always satisfied for any feasible GSIP resulting from the reformulation of a min–max program. In Reference it is also assumed that a solution for the equality constraints exists and that it is unique.…”

Section: Brute Force Solution Methodsmentioning

confidence: 96%

“…At each sampling point v m in the host set V we formulate and then solve the bilevel problem identical to the second‐level problem Equations with the exception that now v comes from a discrete set and is not continuous. The bilevel problem Equations can be reformulated as a GSIP and solved using the algorithm proposed by Djelassi et al with a specialization of the algorithm to min–max problems as proposed in Reference . The smallest worst‐case process cost

Φ_{U}^{*} ((), {bold-italicv}_{normalm}^{*})

is then chosen as the optimal solution value among all the discrete worst‐case realizations.…”

Section: Brute Force Solution Methodsmentioning

confidence: 99%

“…The same bilevel OED formulation was used in Reference , however, using a generalized semi‐infinite program (GSIP) to solve the problem. The method proposed in Reference can guarantee a global solution for the upper‐level and lower‐level problems. In Reference it was shown that even if the upper level cannot be solved globally, a global upper bound is still obtained, as long as the lower level is solved to global optimality.…”

Section: Oed For Bounded‐error Measurementsmentioning

confidence: 99%

“…However, this reformulation cannot guarantee a global solution of the lower level and, therefore, cannot guarantee a feasible solution in the upper level. The same bilevel OED formulation was used in Reference , however, using a generalized semi‐infinite program (GSIP) to solve the problem. The method proposed in Reference can guarantee a global solution for the upper‐level and lower‐level problems.…”

Section: Oed For Bounded‐error Measurementsmentioning

confidence: 99%

“…The method proposed in Reference can guarantee a global solution for the upper‐level and lower‐level problems. In Reference it was shown that even if the upper level cannot be solved globally, a global upper bound is still obtained, as long as the lower level is solved to global optimality. Herein, we adapt the formulation and solution method from Walz et al

ℱ^{*} = normalℱ ((),, {bold-italicv}^{*}, {bold-italicp}^{*}) = \min_{bold-italicv \in V} \max_{\begin{array}{c} p^{L, i} \in P \\ p^{U, i} \in P \end{array}} \sum_{i = 1}^{n_{p}} ((), p_{i}^{U, i} - p_{i}^{L, i})

st .

(},, 2 e_{k}^{\min} \leq g_{k} ((), bold-italicv, \overset{p}{true}) - g_{k} false(bold-italicv, p^{j, i} false) \leq 2 e_{k}^{\max}) \begin{matrix} lefttrue \\ \forall j \in \{U, L\}, i \in \{1, \dots, n_{p}\}, \\ \forall k \in \{1, \dots, n_{y}\} \end{matrix}

with

p^{L, i} = {(p_{1}^{L, i}, \dots, p_{n_{p}}^{L, i})}^{T}

and

p^{U, i} = {(p_{1}^{U, i}, \dots, p_{n_{p}}^{U, i})}^{T}

for i = 1… n p .…”

Section: Oed For Bounded‐error Measurementsmentioning

confidence: 99%

See 4 more Smart Citations

Optimal experimental design for optimal process design: A trilevel optimization formulation

2019

Self Cite

View full text Add to dashboard Cite

Typical optimal experimental design (OED) methods aim at minimizing the covariance matrix of the estimated parameters regardless of the intended application of the model that is being estimated. This can unnecessarily increase the experimental costs. Herein, we propose a new OED method, which tailors the designed experiments to the model application. The method is demonstrated for model-based process design and aims at mitigating a worst-case realization of the process design. The proposed formulation results in a min-max-min problem and is based on boundederror OED. The method is illustrated via an ad hoc solution method using two examples, a simple illustrative example and the van de Vusse reaction, that show the differences between typical and the new tailored OED method: experimental designs can be considered good using the latter method, while the same design would be considered bad with the former methods.

show abstract

Section: Brute Force Solution Methodsmentioning

confidence: 96%

Φ_{U}^{*} ((), {bold-italicv}_{normalm}^{*})

is then chosen as the optimal solution value among all the discrete worst‐case realizations.…”

Section: Brute Force Solution Methodsmentioning

confidence: 99%

Section: Oed For Bounded‐error Measurementsmentioning

confidence: 99%

Section: Oed For Bounded‐error Measurementsmentioning

confidence: 99%

ℱ^{*} = normalℱ ((),, {bold-italicv}^{*}, {bold-italicp}^{*}) = \min_{bold-italicv \in V} \max_{\begin{array}{c} p^{L, i} \in P \\ p^{U, i} \in P \end{array}} \sum_{i = 1}^{n_{p}} ((), p_{i}^{U, i} - p_{i}^{L, i})

st .

(},, 2 e_{k}^{\min} \leq g_{k} ((), bold-italicv, \overset{p}{true}) - g_{k} false(bold-italicv, p^{j, i} false) \leq 2 e_{k}^{\max}) \begin{matrix} lefttrue \\ \forall j \in \{U, L\}, i \in \{1, \dots, n_{p}\}, \\ \forall k \in \{1, \dots, n_{y}\} \end{matrix}

with

p^{L, i} = {(p_{1}^{L, i}, \dots, p_{n_{p}}^{L, i})}^{T}

and

p^{U, i} = {(p_{1}^{U, i}, \dots, p_{n_{p}}^{U, i})}^{T}

for i = 1… n p .…”

Section: Oed For Bounded‐error Measurementsmentioning

confidence: 99%

See 3 more Smart Citations

Optimal experimental design for optimal process design: A trilevel optimization formulation

2019

Self Cite

View full text Add to dashboard Cite

show abstract

Semi-infinite programming for global guarantees of robust fault detection and isolation in safety-critical systems

Hale

Wilhelm

Palmer

et al. 2019

Computers & Chemical Engineering

View full text Add to dashboard Cite

Dynamic real-time optimization of batch processes using Pontryagin’s minimum principle and set-membership adaptation

Paulen

Fikar

2019

Computers & Chemical Engineering

View full text Add to dashboard Cite

This paper studies a dynamic real-time optimization in the context of modelbased time-optimal operation of batch processes under parametric model mismatch. In order to tackle the model-mismatch issue, a receding-horizon policy is usually followed with frequent re-optimization. The main problem addressed in this study is the high computational burden that is usually required by such schemes. We propose an approach that uses parameterized conditions of optimality in the adaptive predictive-control fashion. The uncertainty in the model predictions is treated explicitly using reachable sets that are projected into the optimality conditions. Adaptation of model parameters is performed online using set-membership estimation. A class of batch membrane separation processes is in the scope of the presented applications, where the benefits of the presented approach are outlined.

show abstract

Bounded-error optimal experimental design via global solution of constrained min–max program

Cited by 16 publications

References 37 publications

Optimal experimental design for optimal process design: A trilevel optimization formulation

Optimal experimental design for optimal process design: A trilevel optimization formulation

Semi-infinite programming for global guarantees of robust fault detection and isolation in safety-critical systems

Dynamic real-time optimization of batch processes using Pontryagin’s minimum principle and set-membership adaptation

Contact Info

Product

Resources

About