Temat: equilibrium problem

Skocz do pozycji: 1.

Tytuł:: On the implicit programming approach in a class of mathematical programs with equilibrium constraints
Autorzy:: Outrata, J. V.
Cervinka, M.
Tematy:: mathematical problem with equilibrium constraint
state constraints
implicit programming
calmness
exact penalization; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/970748.pdf Link otwiera się w nowym oknie
Opis:: In the paper we analyze the influence of implicit programming hypothesis and presence of state constraints on first order optimality conditions to mathematical programs with equilibrium constraints. In the absence of state constraints, we derive sharp stationarity conditions, provided the strong regularity condition holds. In the second part of the paper we suggest an exact penalization of state constraints and test the behavior of standard bundle trust region algorithm on academic examples.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On some optimization problem related to economic equilibrium
Autorzy:: Naniewicz, Z.
Tematy:: dwoistość
nierówność wariacyjna
problem optymalizacji
równowaga
duality
equilibrium
optimization problem
variational inequalities; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/1839186.pdf Link otwiera się w nowym oknie
Opis:: The paper considers an optimization problem in which the minima of a finite collection of objective functions satisfy some unilateral constraints and are linked together by a certain subdifferential relationship. The governing relations are stated as a variational inequality defined on a nonconvex feasible set. By the reduction to the variational inequality involving nonmonotone multivalued mapping, defined over nonnegative orthant, the existence of solutions is examined. The prototype is the general economic equilibrium problem. The exemplification of the theory for the quadratic multi-objective function is provided.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: A Nash equilibrium approach for multiobjective optimal control problems with elliptic partial diﬀerential equations
Autorzy:: Dreves, A.
Tematy:: multiobjective optimization
generalized Nash equilibrium
optimal control problem
elliptic partial diﬀerential equation
finite elements
interior point method; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/206122.pdf Link otwiera się w nowym oknie
Opis:: We consider the generalized Nash equilibrium as a solution concept for multiobjective optimal control problems governed by elliptic partial diﬀerential equations with constraints not only for the control but also for the state variables. In the ﬁrst part, we present a constructive proof of the existence of a generalized Nash equilibrium via an approximating sequence of suitable ﬁnite dimensional discretizations. In the second part, we propose a variant of a potential reduction algorithm for the numerical solution of these discretized problems. In contrast to the existing numerical approaches ours does not require the computation of the control–to–state mapping. Instead we introduce diﬀerent state variables and guarantee that they become equal at a solution. We prove suﬃcient conditions for the convergence of our algorithm to a solution. Furthermore, some numerical results showing the applicability are provided.
Dostawca treści:: Biblioteka Nauki

Artykuł

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