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In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…
We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…
In this paper, we consider a finite-dimensional optimization problem minimizing a continuous objective on a compact domain subject to a multi-dimensional constraint function. For the latter, we assume the availability of a global Lipschitz…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
In this paper we consider the problem of optimization of approximate integration of set-valued functions from the class defined by given majorant of their moduli of continuity, using values of the functions at $n$ fixed or free points of…
In this paper, we investigate the concept of p-convexity for sets and functions in n-dimensional Euclidean space. We establish novel algebraic and topological results within this generalized convexity framework. Furthermore, we analyze…
Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such…
In this paper, we discuss a class of spectral partition problems with a measure constraint, for partitions of a given bounded connected open set. We establish the existence of an optimal open partition, showing that the corresponding…
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's…
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…
Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI.…
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…
We consider a misspecified optimization problem that requires minimizing of a convex function $f(x;\theta^*)$ in x over a constraint set represented by $h(x;\theta^*)\leq 0$, where $\theta^*$ is an unknown (or misspecified) vector of…
This chapter presents a self-contained approach of variational analysis and generalized differentiation to deriving necessary optimality in problems of bilevel optimization with Lipschitzian data. We mainly concentrate on optimistic models,…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Rough set is one of the important methods for rule acquisition and attribute reduction. The current goal of rough set attribute reduction focuses more on minimizing the number of reduced attributes, but ignores the spatial similarity…