Related papers: A note on partial calmness for bilevel optimizatio…
In this paper, we establish the lower semicontinuity of the solution mapping and of the approximate solution mapping for parametric fixed point problems under some suitable conditions. As applications, the lower semicontinuity result…
This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the…
The well-posedness of a system of partial differential equations and dynamic boundary conditions, both of Cahn-Hilliard type, is discussed. The existence of a weak solution and its continuous dependence on the data are proved using a…
Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex…
Near-optimality robustness extends multilevel optimization with a limited deviation of a lower level from its optimal solution, anticipated by higher levels. We analyze the complexity of near-optimal robust multilevel problems, where…
Solution methods for generalized Nash equilibrium have been dominated by variational inequalities and complementarity problems. Since these approaches fundamentally rely on the sufficiency of first-order optimality conditions for the…
The paper utilizes H\"older graphical derivatives for characterizing H\"older strong subregularity, isolated calmness and sharp minimum. As applications, we characterize H\"older isolated calmness in linear semi-infinite optimization and…
Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden…
First, a new sufficient condition for uniqueness of weak solutions is proved for the system of 2D viscous Primitive Equations. Second, global existence and uniqueness are established for several classes of weak solutions with partial…
We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…
Calibrations are a possible tool to validate the minimality of a certain candidate. They have been introduced in the context of minimal surfaces and adapted to the case of Steiner problem in several variants. Our goal is to compare the…
Designing high-performance electric machines that maintain their efficiency and reliability under uncertain material and operating conditions is crucial for industrial applications. In this paper, we present a novel framework for robust…
In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…
We consider a new hierarchy of semidefinite relaxations for the general polynomial optimization problem $(P):\:f^{\ast}=\min \{\,f(x):x\in K\,\}$ on a compact basic semi-algebraic set $K\subset\R^n$. This hierarchy combines some advantages…
This paper studies minimizing solutions to a two dimensional Allen-Cahn system on the upper half plane, subject to Dirichlet boundary conditions, \begin{equation*} \Delta u-\nabla_u W(u)=0, \quad u: \mathbb{R}_+^2\to \mathbb{R}^2,\ u=u_0…
When faced with multiple minima of an "inner-level" convex optimization problem, the convex bilevel optimization problem selects an optimal solution which also minimizes an auxiliary "outer-level" convex objective of interest. Bilevel…
The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newton's method. This approach however is usually computationally…
It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and…
In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the…