Related papers: A solution method for arbitrary polyhedral convex …
We consider the problem of choosing prices of a set of products so as to maximize profit, taking into account self-elasticity and cross-elasticity, subject to constraints on the prices. We show that this problem can be formulated as…
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational…
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…
Convexification is a core technique in global polynomial optimization. Currently, there are two main approaches competing in theory and practice: the approach of nonlinear programming and the approach based on positivity certificates from…
Generalized polyhedral convex sets, generalized polyhedral convex functions on locally convex Hausdorff topological vector spaces, and the related constructions such as sum of sets, sum of functions, directional derivative, infimal…
Let $P$ be a set of $n$ labeled points in the plane. The radial system of $P$ describes, for each $p\in P$, the order in which a ray that rotates around $p$ encounters the points in $P \setminus \{p\}$. This notion is related to the order…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…
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…
An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal problems for ordered and convex geometric graphs have a rich…
We consider the following geometric optimization problem: find a maximum-area rectangle and a maximum-perimeter rectangle contained in a given convex polygon with $n$ vertices. We give exact algorithms that solve these problems in time…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
We consider the problem of minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. In order to solve the problem, an algorithm combining the incremental proximal gradient method with…
Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient…
Motivated by the fact that not all nonconvex optimization problems are difficult to solve, we survey in this paper three widely-used ways to reveal the hidden convex structure for different classes of nonconvex optimization problems.…
In this paper, we consider gradient-type methods for convex positively homogeneous optimization problems with relative accuracy. An analogue of the accelerated universal gradient-type method for positively homogeneous optimization problems…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
The problem of minimizing the difference of two lower semicontinuous, proper, convex functions (a DC function) on a nonempty closed convex set in a locally convex Hausdorff topological vector space is studied in this paper. The focus is…
This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices $\text{SO}(n)$. Such problems are nonconvex due to the constraint $X \in \text{SO}(n)$. Nonetheless, we show…