Related papers: First Order Conditions for Semidefinite Representa…
We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper…
In this work, we present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. Convexity prior is very useful for object completion in computer…
The deformability condition for submanifolds of fixed degree immersed in a graded manifold can be expressed as a system of first order PDEs. In the particular but important case of ruled submanifolds, we introduce a natural choice of…
A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). This is done by decomposing a SDFP into smaller problems, in a way that preserves most feasibility properties of the original…
In this paper we study the representation theory of three monoids of partial functions on an $n$-set. The monoid of all order-preserving functions (i.e., functions satisfying $f(x)\leq f(y)$ if $x\leq y$) the monoid of all order-decreasing…
In this paper, we consider an extended concept of invariant for polynomial dynamical system (PDS) with domain and initial condition, and establish a sound and complete criterion for checking semi-algebraic invariants (SAI) for such PDSs.…
Partial label learning deals with the problem where each training instance is assigned a set of candidate labels, only one of which is correct. This paper provides the first attempt to leverage the idea of self-training for dealing with…
In semialgebraic geometry, projections play a prominent role. A definable choice is a semialgebraic selection of one point in every fiber of a projection. Definable choices exist by semialgebraic triviality, but their complexity depends…
We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite…
A partially ordered set P is representable if there is a bounded distributive lattice such that its ordered set of prime ideals is order-isomorphic to P. We show that if the order components of a poset P are representable, then so is P.…
For a principal ideal domain $A$, the Latimer--MacDuffee correspondence sets up a bijection between the similarity classes of matrices in $\operatorname{M}_{n}(A)$ with irreducible characteristic polynomial $f(x)$ and the ideal classes of…
Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing.…
The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and…
We study the convex hull of $SO(n)$, thought of as the set of $n\times n$ orthogonal matrices with unit determinant, from the point of view of semidefinite programming. We show that the convex hull of $SO(n)$ is doubly spectrahedral, i.e.…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
Let $1\leq q\leq (n-1)$. We first show that a necessary condition for a Hankel operator on $(0,q-1)$-forms on a convex domain to be compact is that its symbol is holomorphic along $q$-dimensional analytic varieties in the boundary. Because…
The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold…