Related papers: Von Neumann's minimax theorem through Fourier-Motz…
We introduce a randomized algorithm for computing the minimal-norm solution to an underdetermined system of linear equations. Given an arbitrary full-rank m x n matrix A with m<n, any m x 1 vector b, and any positive real number epsilon…
In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve…
We give a simple proof of the existence of a minimizer for the Sobolev inequality. Our proof is based on a representation formula via a cut-off fundamental solution.
Dantzig and Eaves claimed that fundamental duality theorems of linear programming were a trivial consequence of Fourier elimination. Another property of Fourier elimination is considered here, regarding the existence of implicit equalities…
We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools from matrix theory, (analytic) optimization theory and…
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…
When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this…
We present an optimization problem emerging from optimal control theory and situated at the intersection of fractional programming and linear max-min programming on polytopes. A na\"ive solution would require solving four nested, possibly…
A simple method has been introduced to furnish the equilibrium solution of the Wigner equation for all order of the quantum correction. This process builds up a recursion relation involving the coefficients of the different power of the…
In this paper, we establish a priori estimates for a class of fully nonlinear equations with Neumann boundary conditions. By the continuity method, we have obtained the existence theorem for the Neumann problem.
Given $n \times n$ real symmetric matrices $A_1, \dots, A_m$, the following {\it spectral minimax} property holds: $$\min_{X \in \mathbf{\Delta}_n} \max_{y \in S_m} \sum_{i=1}^m y_iA_i \bullet X=\max_{y \in S_m} \min_{X \in…
Convergence of the classical Newton's method and its DSM version for solving operator equations $F(u)=h$ is proved without any smoothness assumptions on $F'(u)$. It is proved that every solvable equation $F(u)=f$ can be solved by Newton's…
We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.
We are concerned with the tensor equation with an M-tensor or Z-tensor, which we call the M- tensor equation or Z-tensor equation respectively. We derive a necessary and sufficient condition for a Z (or M)-tensor equation to have…
Existence of solutions to doubly nonlinear equations in reflexive Banach spaces is established by resorting to a global-in-time variational approach inspired by De Giorgi's principle, which characterizes the associated flows as…
In this article we consider a method for proving a class of analytical inequalities via minimax rational approximations. All numerical calculations in this paper are given by Maple computer program.
In order to nd a non-negative solution to a system of inequalities, the corresponding dual problem is composed, which has a suitable unity basic matrix. In such a formulation, the objective function is replaced by set of constraints based…
We use the work of Milton, Seppecher, and Bouchitt\'{e} on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In…
We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max…
We prove an easy version of the minimax theorem with no topological assumption. We deduce from it some domination criteria as well as an application to $p$-summing operators.