Related papers: Projection of polyhedral cones and linear vector o…

A polynomial optimization problem (POP) consists of minimizing a multivariate real polynomial on a semi-algebraic set $K$ described by polynomial inequalities and equations. In its full generality it is a non-convex, multi-extremal,…

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…

In this paper we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in [J. F. Bonnans and H. Ram\'irez C., Math. Program. 104 (2005), no. 2-3, Ser. B,…

A convex optimization problem in conic form involves minimizing a linear functional over the intersection of a convex cone and an affine subspace. In some cases, it is possible to replace a conic formulation using a certain cone, with a…

We present a geometrical analysis on the completely positive programming reformulation of quadratic optimization problems and its extension to polynomial optimization problems with a class of geometrically defined nonconvex conic programs…

Differential positivity and K-cooperativity, a special case of differential positivity, extend differential approaches to control to nonlinear systems with multiple equilibria, such as switches or multi-agent consensus. To apply this…

We analyze self-dual polyhedral cones and prove several properties about their slack matrices. In particular, we show that self-duality is equivalent to the existence of a positive semidefinite (PSD) slack. Beyond that, we show that if the…

We show that the minimum distance projection in the L1-norm from an interior point onto the boundary of a convex set is achieved by a single, unidimensional projection. Application of this characterization when the convex set is a…

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…

In this paper, we deal with the problem of optimizing a black-box smooth function over a full-dimensional smooth convex set. We study sets of feasible curves that allow to properly characterize stationarity of a solution and possibly carry…

In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…

A symmetric matrix $A$ is completely positive (CP) if there exists an entrywise nonnegative matrix $V$ such that $A = V V ^T$. In this paper, we study the CP-matrix approximation problem of projecting a matrix onto the intersection of a set…

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…

We study the two-dimensional geometric knapsack problem for convex polygons. Given a set of weighted convex polygons and a square knapsack, the goal is to select the most profitable subset of the given polygons that fits non-overlappingly…

Let A be a finite subset of N^n and R[x]_A be the space of real polynomials whose monomial powers are from A. Let K be a compact basic semialgebraic set of R^n such that R[x]_A contains a polynomial that is positive on K. Denote by P_A(K)…

Semidefinite programming is a fundamental problem class in convex optimization, but despite recent advances in solvers, solving large-scale semidefinite programs remains challenging. Generally the matrix functions involved are spectral or…

An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices.…

This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…

In this thesis, we present results related to complementarity problems. We study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed…

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…