Related papers: The Projection Problem in Commutative, Positively …
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
$(1)$ Let $M\subset N$ be a commutative cancellative torsion-free and subintegral extension of monoids. Then we prove that in the case of ring extension $A[M]\subset A[N]$, the two notions, subintegral and weakly subintegral coincide…
Let $M$ be a monoid that is embeddable in a group. We consider the topos $\mathbf{PSh}(M)$ of sets equipped with a right $M$-action, and we study the subtoposes that are of monoid type, i.e. the subtoposes that are again of the form…
Submodularity is an important concept in integer and combinatorial optimization. A classical submodular set function models the utility of selecting homogenous items from a single ground set, and such selections can be represented by binary…
We firstly prove the completeness of the category of crossed modules in a modified category of interest. Afterwards, we define pullback crossed modules and pullback cat$^1$-objects that are both obtained by pullback diagrams with extra…
A conic program is the problem of optimizing a linear function over a closed convex cone intersected with an affine preimage of another cone. We analyse three constraint qualifications, namely a Closedness CQ, Slater CQ, and Boundedness CQ…
Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
A special inverse monoid is one defined by a presentation where all the defining relations have the form $r = 1$. By a result of Ivanov Margolis and Meakin the word problem for such an inverse monoid can often be reduced to the word problem…
It is well-known that the intersection of the matching polytope with a cardinality constraint is integral [8]. We prove a similar result for the polytope corresponding to the transportation problem with market choice (TPMC) (introduced in…
The closed one-sided ideals of a C*-algebra are exactly the closed subspaces supported by the orthogonal complement of a closed projection. Let A be a (not necessarily selfadjoint) subalgebra of a unital C*-algebra B which contains the unit…
Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…
Working over the field of order 2 we consider those complete caps (maximal sets of points with no three collinear) which are disjoint from some codimension 2 subspace of projective space. We derive restrictive conditions which such a cap…
The classical convex feasibility problem in a finite dimensional Euclidean space is studied in the present paper. We are interested in two cases. First, we assume to know how to compute an exact project onto one of the sets involved and the…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
We study the closure of the locus of radical ideals in the multigraded Hilbert scheme associated with a standard graded polynomial ring and the Hilbert function of a homogeneous coordinate ring of points in general position in projective…
A commutative monoid $M$ is called a linearly orderable monoid if there exists a total order on $M$ that is compatible with the monoid operation. The finitary power monoid of a commutative monoid $M$ is the monoid consisting of all nonempty…
Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…
We introduce an extended tangent cone of high order to a set and study its properties. Then we use this local approximation for deriving high-order necessary conditions for local minimizers of constrained optimization problems.
In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…