相关论文: Multi-cover Inequalities for Totally-Ordered Multi…
Optimizing a nonlinear function over nonconvex sets is challenging since solving convex relaxations may lead to substantial relaxation gaps and infeasible solutions that must be "rounded" to feasible ones, often with uncontrollable losses…
We study a generalization of the knapsack problem with geometric and vector constraints. The input is a set of rectangular items, each with an associated profit and $d$ nonnegative weights ($d$-dimensional vector), and a square knapsack.…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
In this paper, we investigate the mixed-integer nonlinear set with box constraints $X = \{(w,x)\in R\times Z^n:w\leq f(a^Tx),0\leq x\leq \mu\}$, where $f$ is a univariate concave function, $a\in R^n$, and $\mu\in Z^n_{++}$. This set arises…
The unbounded knapsack problem with bounded weights is a variant of the well-studied variant of the traditional binary knapsack problem; key changes being the relaxation of the binary constraint and allowing the unit weights of each item to…
This paper presents an alternate choice of computing the convex hulls (CHs) for planar point sets. We firstly discard the interior points and then sort the remaining vertices by x- / y- coordinates separately, and later create a group…
Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…
A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are…
We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous variables is supermodular. Although supermodular minimization is, in general, difficult,…
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…
In this paper, we investigate several subsets of $n$-copulas and $n$-quasi-copulas from the perspective of convex-lineability and the recently introduced concept of convex-spaceability. Our purpose is to determine when such families contain…
We consider multi-commodity network design models, where capacity can be added to the arcs of the network using multiples of facilities that may have different capacities. This class of mixed-integer optimization models appears frequently…
A variant of the well-known Knapsack Problem is studied in this paper, where pairs of items are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which can be used to model real…
We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…
We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…
Packing problems constitute an important class of optimization problems, both because of their high practical relevance and theoretical appeal. However, despite the large number of variants that have been studied in the literature, most…
Recent advances in the efficiency and robustness of algorithms solving convex quadratically constrained quadratic programming (QCQP) problems motivate developing techniques for creating convex quadratic relaxations that, although more…
Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum…
We introduce methods to count and enumerate all maximal independent, all maximum independent sets, and all independent sets in threshold graphs and k-threshold graphs. Within threshold graphs and k-threshold graphs independent sets…
We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple…