Related papers: On the Stationary Duality of Structural Composite …
A memory-efficient framework is described for the cardinality-constrained structured data-fitting problem. Dual-based atom-identification rules are proposed that reveal the structure of the optimal primal solution from near-optimal dual…
We study cardinality-constrained optimization problems (CCOP) in general position, i. e. those optimization-related properties that are fulfilled for a dense and open subset of their defining functions. We show that the well-known…
The cardinality constrained optimization problem (CCOP) is an optimization problem where the maximum number of nonzero components of any feasible point is bounded. In this paper, we consider CCOP as a mathematical program with disjunctive…
We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
Binary polynomial optimization is equivalent to the problem of minimizing a linear function over the intersection of the multilinear set with a polyhedron. Many families of valid inequalities for the multilinear set are available in the…
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable…
This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields (CUP) for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis…
Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems…
Optimization - minimization or maximization - in the lattice of subsets is a frequent operation in Artificial Intelligence tasks. Examples are subset-minimal model-based diagnosis, nonmonotonic reasoning by means of circumscription, or…
The canonical duality theory has provided with a unified analytic solution to a range of discrete and continuous problems in global optimization, which can transform a nonconvex primal problem to a concave maximization dual problem over a…
We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the…
We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…
Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems…
We consider ordinal online problems, i.e., tasks that only require pairwise comparisons between elements of the input. A classic example is the secretary problem and the game of googol, as well as its multiple combinatorial extensions such…
Indicator functions of taking values of zero or one are essential to numerous applications in machine learning and statistics. The corresponding primal optimization model has been researched in several recent works. However, its dual…
In the Constraint Satisfaction Problem (CSP for short) the goal is to decide the existence of a homomorphism from a given relational structure $G$ to a given relational structure $H$. If the structure $H$ is fixed and $G$ is the only input,…