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The Generalized Euler-Lagrange and Hamiltonian Inclusion Conditions
The subject matter of this chapter is necessary conditions of optimality for differential inclusion problems, by which we mean dynamic optimization...
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The Euler-Lagrange and Hamiltonian Inclusion Conditions in the Presence of State Constraints
This chapter concerns necessary conditions of optimality for dynamic optimization problems with pathwise state constraints, when the dynamic...
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Refined Euler–Lagrange Inclusion for an Optimal Control Problem with Discontinuous Integrand
AbstractWe study a free-time optimal control problem for a differential inclusion with mixed-type functional in which the integral term contains the...
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On selections of set-valued Euler-Lagrange inclusions with applications
We discuss the set-valued dynamics related to the theory of functional equations. We look for selections of convex set-valued functions satisfying...
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Optimization of the Dirichlet problem for gradient differential inclusions
The paper is devoted to optimization of the gradient differential inclusions (DFIs) on a rectangular area. The discretization method is the main...
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Hamiltonian Systems
In this chapter we explain the origin of symplectic geometry, i.e., classical mechanics. For this, first we review some background about flows of...
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Optimization of Higher-Order Differential Inclusions with Special Boundary Value Conditions
The paper is devoted to Lagrange problem of optimal control theory with higher-order differential inclusions (HODI) and special boundary conditions....
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The Maximum Principle for Problems with Pathwise Constraints
This chapter provides necessary conditions of optimality for dynamic optimization problems involving pathwise constraints. Attention is directed at...
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Duality in the problems of optimal control described by Darboux-type differential inclusions
This paper is devoted to the optimization of the Mayer problem with hyperbolic differential inclusions of the Darboux type and duality. We use the...
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Optimization of boundary value problems for higher order differential inclusions and duality
The paper is mainly devoted to the theory of duality of boundary value problems (BVPs) for differential inclusions of higher orders. For this, on the...
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Regularity of Minimizers
This chapter provides conditions under which minimizers for dynamic optimization problems possess regularity properties of interest, such as...
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Defense-Critical Supply Chain Networks and Risk Management with the Inclusion of Labor: Dynamics and Quantification of Performance and the Ranking of Nodes and Links
The efficient and effective performance of defense-critical supply chain networks is essential to both national and global security. Disruptions to...
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Study on wave dispersion characteristics of piezoelectric sandwich nanoplates considering surface effects
In this study, the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed...
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A note on the supersolution method for Hardy’s inequality
We prove a characterization of Hardy’s inequality in Sobolev–Slobodeckiĭ spaces in terms of positive local weak supersolutions of the relevant...
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Some non-linear systems of PDEs related to inverse problems in conductivity
We study some non-linear systems of PDEs that turn out to be related to the classical inverse problem in conductivity. They have a variational...
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Free End-Time Problems
This chapter provides necessary conditions of optimality for free end-time dynamic optimization problems, that is problems in which the left and...
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Duality Problems with Second-Order Polyhedral Discrete and Differential Inclusions
The present paper deals with the theory of duality for the Mayer problem given by second-order polyhedral discrete and differential inclusions....
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The Addition of Vortices
The symplectic and Poisson formulations of point vortex and vortex rings models, mainly due to Marsden and Weinstein (Physica D 7:305–323, 1983), are...
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Unified Discrete Multisymplectic Lagrangian Formulation for Hyperelastic Solids and Barotropic Fluids
We present a geometric variational discretization of nonlinear elasticity in 2D and 3D in the Lagrangian description. A main step in our construction...
