Related papers: Strong Duality Theorem for Continuous-Time Linear …
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory…
This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…
Farkas established that a system of linear inequalities has a solution if and only if we cannot obtain a contradiction by taking a linear combination of the inequalities. We state and formally prove several Farkas-like theorems over…
We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depends on the uncertainty parameter. The interest of our…
We study nonconvex quadratic problems (QPs) with quadratic separable constraints, where these constraints can be defined both as inequalities or equalities. We derive sufficient conditions for these types of problems to present the…
In this article, we present semi strongly $E$-preinvexity and semi strongly $E$-invexity. To demonstrate the existence of these functions, certain nontrivial examples have been developed. Several significant relationships and…
A new approach to linear programming duality is proposed which relies on quadratic penalization, so that the relation between solutions to the penalized primal and dual problems becomes affine. This yields a new proof of Levin's duality…
We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of…
This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently proposed…
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…
In this paper we present two Fenchel-type dual problems for a DC (difference of convex functions) optimization primal one. They have been built by means of the c-conjugation scheme, a pattern of conjugation which has been shown to be…
The strict complementary slackness condition (SCSC) is an important concept in the duality theory of linear programming (LP). The current study aims at extending this concept to the framework of linear fractional programming (LFP). First,…
For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof…
We present a new kind of Lagrangian duality theory for set-valued convex optimization problems whose objective and constraint maps are defined between preordered normed spaces. The theory is accomplished by introducing a new set-valued…
Suppose that f is a function from Z_p -> [0,1] (Z_p is my notation for the integers mod p, not the p-adics), and suppose that a_1,...,a_k are some places in Z_p. In some additive number theory applications it would be nice to perturb f…
The aim of this paper is to revisit some duality results in conic linear programming and to answer an open problem related to the duality gap function for Gale's example.
We consider a mathematical model for the classical Sudoku puzzle, which we call the primal problem and introduce a corresponding dual problem. Both problems are constraint satisfaction models and a duality relation between them is proved.…