Existence of viable solutions for nonconvex differential inclusions.
Existence results for first and second order nonconvex sweeping process with delay.
Existence results for general inequality problems with constraints.
Existence results of nonconvex differential inclusions.
Existence Theorems for the Dirichlet Elliptic Inclusion Involving Exponential-Growth-Type Multivalued Right-Hand Side
We present two existence results for the Dirichlet elliptic inclusion with an upper semicontinuous multivalued right-hand side in exponential-type Orlicz spaces involving a vector Laplacian, subject to Dirichlet boundary conditions on a domain Ω⊂ ℝ². The first result is obtained via the multivalued version of the Leray-Schauder principle together with the Nakano-Dieudonné sequential weak compactness criterion. The second result is obtained by using the nonsmooth variational technique together with...
Extensions of minimization theorems and fixed point theorems on a quasimetric space.
Favorable classes of mappings and multimappings in nonlinear analysis and optimization.
Feedback in state constrained optimal control
An optimal control problem is studied, in which the state is required to remain in a compact set . A control feedback law is constructed which, for given , produces -optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in . The construction relies upon a constraint removal technique which utilizes geometric properties of inner approximations of and a related trajectory tracking result. The control feedback is shown to possess a robustness...
Feedback in state constrained optimal control
An optimal control problem is studied, in which the state is required to remain in a compact set S. A control feedback law is constructed which, for given ε > 0, produces ε-optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in S. The construction relies upon a constraint removal technique which utilizes geometric properties of inner approximations of S and a related trajectory tracking result. The control feedback is shown to possess a robustness...
Finding global minima with a filled function approach for non-smooth global optimization.
First Order Characterizations of Pseudoconvex Functions
First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.
First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints
2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions, it admits directionally...
Fritz John's type conditions and associated duality forms in convex non differentiable vector-optimization
From scalar to vector optimization
Initially, second-order necessary optimality conditions and sufficient optimality conditions in terms of Hadamard type derivatives for the unconstrained scalar optimization problem , , are given. These conditions work with arbitrary functions , but they show inconsistency with the classical derivatives. This is a base to pose the question whether the formulated optimality conditions remain true when the “inconsistent” Hadamard derivatives are replaced with the “consistent” Dini derivatives. It...
General comparison principle for variational-hemivariational inequalities.
General existence results for second order nonconvex sweeping process with unbounded perturbations.
Generalized directional derivatives for locally Lipschitz functions which satisfy Leibniz rule
Generalized gradient flow and singularities of the Riemannian distance function
Significant information about the topology of a bounded domain of a Riemannian manifold is encoded into the properties of the distance, , from the boundary of . We discuss recent results showing the invariance of the singular set of the distance function with respect to the generalized gradient flow of , as well as applications to homotopy equivalence.
Generalized gradients for locally Lipschitz integral functionals on non--type spaces of measurable functions
Let (Ω,μ) be a measure space, E be an arbitrary separable Banach space, be the dual equipped with the weak* topology, and g:Ω × E → ℝ be a Carathéodory function which is Lipschitz continuous on each ball of E for almost all s ∈ Ω. Put . Consider the integral functional G defined on some non--type Banach space X of measurable functions x: Ω → E. We present several general theorems on sufficient conditions under which any element γ ∈ X* of Clarke’s generalized gradient (multivalued C-subgradient)...
Generalized invexities and global minimum properties.