scholarly journals Pitfalls and Remedies in DEA Applications: How to Handle an Occurrence of Zero in Multipliers by Strong Complementary Slackness Conditions

Engineering ◽  
2013 ◽  
Vol 05 (05) ◽  
pp. 29-34 ◽  
Author(s):  
Toshiyuki Sueyoshi ◽  
Mika Goto
Keyword(s):  
Complementary Slackness ◽  
Complementary Slackness Conditions

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

scholarly journals Optimal Bail-Out Dividend Problem with Transaction Cost and Capital Injection Constraint

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 13
Author(s):  
Mauricio Junca ◽  
Harold Moreno-Franco ◽  
José Pérez
Keyword(s):  
Transaction Cost ◽  
Lagrange Multiplier ◽  
Risk Model ◽  
Present Value ◽  
Complementary Slackness ◽  
Numerical Examples ◽  
Capital Injection ◽  
Fixed Transaction Cost ◽  
Bail Out ◽  
Complementary Slackness Conditions

We consider the optimal bail-out dividend problem with fixed transaction cost for a Lévy risk model with a constraint on the expected present value of injected capital. To solve this problem, we first consider the optimal bail-out dividend problem with transaction cost and capital injection and show the optimality of reflected ( c 1 , c 2 ) -policies. We then find the optimal Lagrange multiplier, by showing that in the dual Lagrangian problem the complementary slackness conditions are met. Finally, we present some numerical examples to support our results.

scholarly journals Optimality of refraction strategies for a constrained dividend problem

2019 ◽  
Vol 51 (03) ◽  
pp. 633-666
Author(s):  
Mauricio Junca ◽  
Harold A. Moreno-Franco ◽  
José Luis Pérez ◽  
Kazutoshi Yamazaki
Keyword(s):  
Lebesgue Measure ◽  
Control Strategies ◽  
Risk Models ◽  
Complementary Slackness ◽  
Absolutely Continuous ◽  
Numerical Examples ◽  
Time Of Ruin ◽  
Optimal Dividend ◽  
The Time Of Ruin ◽  
Complementary Slackness Conditions

AbstractWe consider de Finetti’s problem for spectrally one-sided Lévy risk models with control strategies that are absolutely continuous with respect to the Lebesgue measure. Furthermore, we consider the version with a constraint on the time of ruin. To characterize the solution to the aforementioned models, we first solve the optimal dividend problem with a terminal value at ruin and show the optimality of threshold strategies. Next, we introduce the dual Lagrangian problem and show that the complementary slackness conditions are satisfied, characterizing the optimal Lagrange multiplier. Finally, we illustrate our findings with a series of numerical examples.

scholarly journals A note on imposing strong complementary slackness conditions in DEA

2012 ◽  
Vol 220 (3) ◽  
pp. 716-721 ◽  
Author(s):  
Vladimir E. Krivonozhko ◽  
Finn R. Førsund ◽  
Andrey V. Lychev
Keyword(s):  
Complementary Slackness ◽  
Complementary Slackness Conditions
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