Related papers: New Constraint Qualifications for Optimization Pro…
The paper introduces several new concepts for solving nonconvex or nonsmooth optimization problems, including convertible nonconvex function, exact convertible nonconvex function and differentiable convertible nonconvex function. It is…
We study a cardinality-constrained optimization problem with nonnegative variables in this paper. This problem is often encountered in practice. Firstly we study some properties on the optimal solutions of this optimization problem under…
This paper concerns a class of constrained optimization problems in which, the objective and constraint functions are both upper-$\mathcal{C}^2$. For such nonconvex and nonsmooth optimization problems, we develop an inexact moving balls…
It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint linear constraints are very rare. This paper aims to discuss optimality…
In this paper, we study constraint qualifications for the nonconvex inequality defined by a proper lower semicontinuous function. These constraint qualifications involve the generalized construction of normal cones and subdifferentials.…
Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several…
In this paper we consider three minimization problems, namely quadratic, $\rho$-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and…
This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investigate the consistency of optimal values and solutions…
Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness…
This paper is devoted to establishing an enhanced Fritz John type first-order necessary condition for a general constrained nonlinear infinite-dimensional optimization problem. Unlike traditional constraint qualifications in optimization…
The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
This paper is devoted to the study of the metric subregularity constraint qualification (MSCQ) for general optimization problems, with the emphasis on the nonconvex setting. We elaborate on notions of directional pseudo- and…
This paper presents a framework for inverse learning of objective functions for constrained optimal control problems, which is based on the Karush-Kuhn-Tucker (KKT) conditions. We discuss three variants corresponding to different model…
A neural network-based approach for solving parametric convex optimization problems is presented, where the network estimates the optimal points given a batch of input parameters. The network is trained by penalizing violations of the…
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…
Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important practical optimization problems whose feasible regions are…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
In this paper, we study a class of optimization problems, called Mathematical Programs with Cardinality Constraints (MPCaC). This kind of problem is generally difficult to deal with, because it involves a constraint that is not continuous…
We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain…