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We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite…
This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are…
Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them…
Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at…
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…
We present a parallel approximation algorithm for a class of mixed packing and covering semidefinite programs which generalize on the class of positive semidefinite programs as considered by Jain and Yao [2011]. As a corollary we get a…
We present a new simple method for rounding a semidefinite programming relaxation of a constraint satisfaction problem. We apply it to the problem of approximate angular synchronization. Specifically, we are given directed distances on a…
Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…
We consider sensitivity of a semidefinite program under perturbations in the case that the primal problem is strictly feasible and the dual problem is weakly feasible. When the coefficient matrices are perturbed, the optimal values can…
We show that the Christensen-Sinclair factorization theorem, when the underlying Hilbert spaces are finite dimensional, is an instance of strong duality of semidefinite programming. This gives an elementary proof of the result and also…
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…
Semidefinite Optimization has become a standard technique in the landscape of Mathematical Programming that has many applications in finite dimensional Quantum Information Theory. This paper presents a way for finite-dimensional relaxations…
Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results either rely on computing sparse…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry…
We introduce a relaxation for homomorphism problems that combines semidefinite programming with linear Diophantine equations, and propose a framework for the analysis of its power based on the spectral theory of association schemes. We use…
This paper is a tutorial in a general and explicit procedure to simplify semidefinite programs which are invariant under the action of a symmetry group. The procedure is based on basic notions of representation theory of finite groups. As…
We obtain a complete characterization of the norm attainment set of a bounded linear functional on a normed space, in terms of a semi-inner-product defined on the space. Motivated by this result, we further apply the concept of…
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
Procrustes problems are matrix approximation problems searching for a~transformation of the given dataset to fit another dataset. They find applications in numerous areas, such as factor and multivariate analysis, computer vision,…