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1

On the multiobjective control problem

Kumar P., Sharma B.

Journal of Applied Analysis

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2018

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Vol. 24, nr 2

223--231

EN

In this paper, sufficient optimality conditions are established for the multiobjective control problem using efficiency of higher order as a criterion for optimality. The ρ-type 1 invex functionals (taken in pair) of higher order are proposed for the continuous case. Existence of such functionals is confirmed by a numer of examples. It is shown with the help of an example that this class is more general than the existing class of functionals.Weak and strong duality theorems are also derived for a mixed dual in order to relate efficient solutions of higher order for primal and dual problems.

2

Dualne liniowe dodatnie układy dyskretne z jednym opóźnieniem

Kociszewski R.

Pomiary Automatyka Robotyka

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2007

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R. 11, nr 2

PL

W pracy rozpatrzono problem dualności liniowych dodatnich układów dyskretnych z jednostkowym opóźnieniem w wektorze stanu. Pokazano, że w ogólnym przypadku dodatnie układy z opóźnieniem nie są układami dualnymi. Aby spełnione były warunki konieczne i wystarczające dualności (tj. równoważność warunków osiągalności i obserwowalności) należy rozpatrywać układy dodatnie z czystym opóźnieniem. Dla tej klasy układów sformułowano kryteria całkowitej osiągalności i całkowitej obserwowalności.

EN

The problem of duality of linear positive discrete-time systems with one delay in state is considered. It is shown that the two positive discrete-time systems are not dual in general case. These systems may be dual only in the case of systems with pure delay. Necessary and sufficient conditions for complete reachability and complete observability of the systems with pure delay are established. A method for computing of the control sequence which transfer the system from zero complete initial state to the desired complete state and method for computing of the output sequence are given.

3

Approximating the solution of a dynamic, stochastic multiple knapsack problem

Hartman J. C., Perry T. C.

Control and Cybernetics

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2006

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Vol. 35, no 3

535-550

EN

We model an environment where orders arrive probabilistically over time, with their revenues and capacity requirements becoming known upon arrival. The decision is whether to accept an order, receiving a reward and reserving capacity, or reject an order, freeing capacity for possible future arrivals. We model the dynamic, stochastic multiple knapsack problem (DSMKP) with stochastic dynamic programming (SDP). Multiple knapsacks are used as orders may stay in the system for multiple periods. As the state space grows exponentially in the number of knapsacks and the number of possible orders per period, we utilize linear programming and duality to quickly approximate the end-of-horizon values for the SDP. This helps mitigate end-of-study effects when solving the SDP directly, allowing for the solution of larger problems and leading to increased quality in solutions.

4

Multiobjective duality for the Markowitz portfolio optimization problem

Wanka G.

Control and Cybernetics

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1999

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Vol. 28, no 4

691-702

EN

The classical Markowitz approach to portfolio selection leads to a biobjective optimization problem where the objectives are the expected return and the variance of a portfolio. In this paper a biobjective dual optimization problem to the Markowitz portfolio optimization problem is introduced and analyzed. For the Markowitz problem and its dual, weak and strong vector duality assertions are derived. The optimality conditions are also verified.