相关论文: Convex and linear models of NP-problems
Low-rank matrix recovery problems are inverse problems which naturally arise in various fields like signal processing, imaging and machine learning. They are non-convex and NP-hard in full generality. It is therefore a delicate problem to…
We characterize the solution to the Newton minimal resistance problem in a class of radial q-concave profiles. We also give the corresponding result for one-dimensional profiles. Moreover, we provide a numerical optimization algorithm for…
In this paper it is shown that the compact linearization approach, that has been previously proposed only for binary quadratic problems with assignment constraints, can be generalized to arbitrary linear equations with positive coefficients…
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
In this paper, we mainly study one class of mixed-integer nonlinear programming problems (MINLPs) with vector conic constraint in Banach spaces. Duality theory of convex vector optimization problems applied to this class of MINLPs is deeply…
Our first result is a statement of a somewhat general form of a non-substitution theorem for linear programming problems, along with a very easy proof of the same. Subsequently, we provide an easy proof of theorem 1 in a 1979 paper of Olvi…
Using the dbar-problem and dual dbar-problem, we derive bilinear relations which allows us to construct integrable hierarchies in different parametrizations, their Darboux-B\"{a}cklund transformations and to analyze constraints for them ina…
We show that linearly constrained linear optimization over a Stiefel or Grassmann manifold is NP-hard in general. We show that the same is true for unconstrained quadratic optimization over a Stiefel manifold. We will show that unless…
We overview the main ideas and techniques of the functional-analytical approach to some extremal problems of convex geometry that stem from the Queen Dido problem.
We apply recent results on semi-classical trace formulae and on Birkhoff normal forms for semi-classical Fourier integral operators to a wide range of semi-classical and high energy spectral inverse problems.
We summarise the recent theoretical progress in few-body descriptions of the piNN system. Previous descriptions, both three- and four-dimensional, are shown to possess serious theoretical inconsistencies. We illustrate how three-dimensional…
A detailed combinatorial analysis of planar convex lattice polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a limit shape when the number of vertices is constrained.
We show uniqueness results for the anisotropic Calder\'{o}n problem stated on transversally anisotropic manifolds. Moreover, we give a convexity result for the range of Dirichlet-to-Neumann maps on general Riemannian manifolds near the zero…
In this paper we take a quasi-Newton approach to nonlinear eigenvalue problems (NEPs) of the type $M(\lambda)v=0$, where $M:\mathbb{C}\rightarrow\mathbb{C}^{n\times n}$ is a holomorphic function. We investigate which types of approximations…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and…
We describe a perturbation method that can be used to reduce the problem of finding the multivariate generating function (MGF) of a non-simple polytope to computing the MGF of simple polytopes. We then construct a perturbation that works…
The Birkhoff's theorem states that any doubly stochastic matrix lies inside a convex polytope with the permutation matrices at the corners. It can be proven that a similar theorem holds for unitary matrices with equal line sums for prime…