Necessary optimality condition for trilevel optimization problem

Topology optimization of quasistatic contact problemsThis paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied by the body in unilateral contact with the rigid foundation to obtain the optimally shaped domain for which the normal contact stress along the contact boundary is minimized. The volume of the body is assumed to be bounded. Using the material derivative and asymptotic expansion methods as well as the results concerning the differentiability of solutions to quasistatic variational inequalities, the topological derivative of the shape functional is calculated and a necessary optimality condition is formulated.

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Derivatives of Hadamard type in vector optimization

Mathematica Slovaca ◽

10.1515/ms-2017-0113 ◽

2018 ◽

Vol 68 (2) ◽

pp. 421-430

Author(s):

Karel Pastor

Keyword(s):

Nonlinear Analysis ◽

Optimality Conditions ◽

Vector Optimization ◽

Optimality Condition ◽

Optimization Problem ◽

Vector Optimization Problem ◽

Dini Derivatives ◽

Scalar Optimality ◽

Derivatives Of

Abstract In our paper we will continue the comparison which was started by Vsevolod I. Ivanov [Nonlinear Analysis 125 (2015), 270–289], where he compared scalar optimality conditions stated in terms of Hadamard derivatives for arbitrary functions and those which was stated for ℓ-stable functions in terms of Dini derivatives. We will study the vector optimization problem and we show that also in this case the optimality condition stated in terms of Hadamard derivatives is more advantageous.

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Optimality of Approximate Quasi-Weakly Efficient Solutions for Vector Equilibrium Problems via Convexificators

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595921500470 ◽

2021 ◽

Author(s):

Guolin Yu ◽

Siqi Li ◽

Xiao Pan ◽

Wenyan Han

Keyword(s):

Optimality Condition ◽

Generalized Convexity ◽

Equilibrium Problems ◽

Efficient Solutions ◽

Sufficient Optimality Condition ◽

Necessary Optimality Condition ◽

Weakly Efficient Solutions ◽

Convexity Assumption ◽

Pseudoconvex Function ◽

Vector Equilibrium

This paper is devoted to the investigation of optimality conditions for approximate quasi-weakly efficient solutions to a class of nonsmooth Vector Equilibrium Problem (VEP) via convexificators. First, a necessary optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is presented by making use of the properties of convexificators. Second, the notion of approximate pseudoconvex function in the form of convexificators is introduced, and its existence is verified by a concrete example. Under the introduced generalized convexity assumption, a sufficient optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is also established. Finally, a scalar characterization for approximate quasi-weakly efficient solutions to problem (VEP) is obtained by taking advantage of Tammer’s function.

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A note on the paper "Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming"

RAIRO - Operations Research ◽

10.1051/ro/2020107 ◽

2020 ◽

Author(s):

Nazih Abderrazzak Gadhi ◽

Aissam Ichatouhane

Keyword(s):

Optimality Conditions ◽

Programming Problem ◽

Optimality Condition ◽

Short Proof ◽

Necessary Optimality Condition ◽

Main Result Theorem ◽

Correct Formulation ◽

Result Theorem ◽

Infinite Programming ◽

Interval Valued

A nonsmooth semi-infinite interval-valued vector programming problem is solved in the paper by Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020066, 2020). The necessary optimality condition obtained by the authors, as well as its proof, is false. Some counterexamples are given to refute some results on which the main result (Theorem 4.5) is based. For the convinience of the reader, we correct the faulty in those results, propose a correct formulation of Theorem 4.5 and give also a short proof.

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A New Sequential Optimality Condition of Cardinality-Constrained Optimization Problem and Application

10.21203/rs.3.rs-878309/v1 ◽

2021 ◽

Author(s):

Liping Pang ◽

Menglong Xue ◽

Na Xu

Keyword(s):

Constrained Optimization ◽

Optimality Condition ◽

Optimization Problem ◽

Constraint Qualification ◽

Accumulation Point ◽

Iterative Sequence ◽

Stationary Points ◽

Constrained Optimization Problem ◽

Cardinality Constraint ◽

Continuous Relaxation

Abstract In this paper, we consider the cardinality-constrained optimization problem and propose a new sequential optimality condition for the continuous relaxation reformulation which is popular recently. It is stronger than the existing results and is still a first-order necessity condition for the cardinality constraint problem without any additional assumptions. Meanwhile, we provide a problem-tailored weaker constraint qualification, which can guarantee that new sequential conditions are Mordukhovich-type stationary points. On the other hand, we improve the theoretical results of the augmented Lagrangian algorithm. Under the same condition as the existing results, we prove that any feasible accumulation point of the iterative sequence generated by the algorithm satisfies the new sequence optimality condition. Furthermore, the algorithm can converge to the Mordukhovich-type (essentially strong) stationary point if the problem-tailored constraint qualification is satisfied.

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Noether’s theorem for fractional variational problems of variable order

Open Physics ◽

10.2478/s11534-013-0208-2 ◽

2013 ◽

Vol 11 (6) ◽

Cited By ~ 16

Author(s):

Tatiana Odzijewicz ◽

Agnieszka Malinowska ◽

Delfim Torres

Keyword(s):

Optimality Condition ◽

Variational Problems ◽

Time Variable ◽

Variable Order ◽

Necessary Optimality Condition ◽

Noether’S Theorem ◽

Noether's Theorem ◽

Fractional Variational Problems ◽

Derivatives Of

AbstractWe prove a necessary optimality condition of Euler-Lagrange type for fractional variational problems with derivatives of incommensurate variable order. This allows us to state a version of Noether’s theorem without transformation of the independent (time) variable. Considered derivatives of variable order are defined in the sense of Caputo.

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A multiplier rule in set-valued optimisation

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700037448 ◽

2003 ◽

Vol 68 (1) ◽

pp. 93-100 ◽

Cited By ~ 13

Author(s):

Akhtar A. Khan ◽

Fabio Raciti

Keyword(s):

Optimality Condition ◽

Necessary Optimality Condition ◽

Dini Derivative ◽

Multiplier Rule

A multiplier rule is given as a necessary optimality condition for proper minimality in set-valued optimisation. We use derivatives in the sense of the lower Dini derivative for the objective set-valued map and the set-valued maps defining the constraints.

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