Related papers: Multilinear Sets with Two Monomials and Cardinalit…
Bi-objective optimization problems on matroids are in general intractable and their corresponding decision problems are in general NP-hard. However, if one of the objective functions is restricted to binary cost coefficients the problem…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…
We consider strongly convex optimization problems with affine-type restrictions. We build dual problem and solve dual problem by Fast Gradient Method. We use primal-dual structure of this method to construct the solution of the primal…
We study the problem of generating monomials of a polynomial in the context of enumeration complexity. In this setting, the complexity measure is the delay between two solutions and the total time. We present two new algorithms for…
We present a novel, general, and unifying point of view on sparse approaches to polynomial optimization. Solving polynomial optimization problems to global optimality is a ubiquitous challenge in many areas of science and engineering.…
In this article, a novel barrier function is introduced to convert the box-constrained convex optimization problem to an unconstrained problem. For each double-sided bounded variable, a single monomial function is added as a barrier…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the…
We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supported on a fixed polyhedral simplicial fan. We investigate…
Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, in terms of Linear Matrix Inequalities and Bilinear…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
A particularly important substructure in modeling joint linear chance-constrained programs with random right-hand sides and finite sample space is the intersection of mixing sets with common binary variables (and possibly a knapsack…
This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of fourth-order polynomial and a log-sum-exp function. Such a problem arises extensively in engineering and sciences. Based…
Consider the closed convex hull $K$ of a monomial curve given parametrically as $(t^{m_1},\ldots,t^{m_n})$, with the parameter $t$ varying in an interval $I$. We show, using constructive arguments, that $K$ admits a lifted semidefinite…
Clustering consists of partitioning data objects into subsets called clusters according to some similarity criteria. This paper addresses a generalization called quasi-clustering that allows overlapping of clusters, and which we link to…
Recently, we proposed a class of inequalities called lifted bilinear cover inequalities, which are second-order cone representable convex inequalities, and are valid for a set described by a separable bilinear constraint together with…
We provide a solution method for the polyhedral convex set optimization problem, that is, the problem to minimize a set-valued mapping with polyhedral convex graph with respect to a set ordering relation which is generated by a polyhedral…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…