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On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization
This paper concentrates on necessary conditions for properly efficient solutions in nonsmooth multiobjective optimization problems. We first present...
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Smooth Solution of Multi-dimensional Nonhomogeneous Conservation Law: Its Formula, and Necessary and Sufficient Blowup Criterion
In this paper, we are concerned with the necessary and sufficient condition of the global existence of smooth solutions of the Cauchy problem of the...
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Unified Robust Necessary Optimality Conditions for Nonconvex Nonsmooth Uncertain Multiobjective Optimization
This paper is concerned with nonconvex nonsmooth uncertain multiobjective optimization problems, in which the decision variable of both objective and...
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A Necessary and Sufficient Condition for the Solvability of the Nonlinear Schrödinger Equation on a Finite Interval
The admissibility of the initial-boundary data, which characterizes the existence of solution for the initial-boundary value problem, is important....
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On Necessary Optimality Conditions for Sets of Points in Multiobjective Optimization
Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend...
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Necessary conditions for turnpike property for generalized linear–quadratic problems
In this paper, we develop several necessary conditions of turnpike property for generalized linear–quadratic (LQ) optimal control problem in...
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A Model of String System Deformations on a Star Graph with Nonlinear Condition at the Node
In this paper, a model of deformations of Stieltjes strings system located along a geometric star graph with a nonlinear condition at the node is...
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Measure Differential Equations with a General Nonlocal Condition
This paper is devoted to study the existence of solutions for a class of measure differential equations –abbreviated, MDEs– with a general nonlocal...
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Multiplicatively Idempotent Semirings with Annihilator Condition
Abstract—The structural theory of semirings with additional conditions is considered. Multiplicatively idempotent semirings with the annihilator...
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On the Weak Second-order Optimality Condition for Nonlinear Semidefinite and Second-order Cone Programming
Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built...
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Controllability and Second-Order Necessary Conditions for Local Infimum Trajectories in Optimal Control
AbstractWe introduce the concept of local controllability of a dynamical system and present sufficient conditions for such controllability. As an...
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Necessary Optimality Conditions for Hybrid System of Variable Dimension with Intermediate Constraints
We consider an optimal control problem for a hybrid system. The continuous motion of the system alternates with discrete variations (switchings) at...
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The Sufficient and Necessary Conditions of the Strong Law of Large Numbers under Sub-linear Expectations
In this paper, by establishing a Borel–Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of...
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Second-order necessary conditions in optimal control of evolution systems
This paper is devoted to second-order necessary optimality conditions for a class of infinite-dimensional optimal control problems under functional ...
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On the Partial Calmness Condition for an Interval-Valued Bilevel Optimization Problem
In this paper, we investigate the necessary optimality conditions for a special bilevel optimization problem in which both the upper and lower level...
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The Necessary and Sufficient Conditions of Exponential Stability for Heat and Wave Equations with Memory
This paper is addressed to a study of the stability of heat and wave equations with memory The necessary and sufficient conditions of the exponential...
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Necessary Conditions in Infinite-Horizon Control Problems that Need no Asymptotic Assumptions
We consider an infinite-horizon optimal control problem with an asymptotic terminal constraint. For the weakly overtaking criterion and the...
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First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition
The well known constant rank constraint qualification [Math. Program. Study 21:110–126, 1984] introduced by Janin for nonlinear programming has been...
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Maxwell–Stokes system with Robin boundary condition
This paper concerns the Maxwell–Stokes system with either curl-Robin boundary condition or mixed curl-Robin boundary condition. While the curl-Robin...