Morse inequalities for diffeomorphisms of a compact manifold were first proved by Smale [21] under the assumption that the nonwandering set is finite. We call these the integral Morse inequalities. They were generalized by Zeeman in an unpublished work cited in [25] to diffeomorphisms with a hyperbolic chain recurrent set that is axiom-A-diffeomorphisms which satisfy the no cycle condition. For...

In this paper we show that finding solutions of a system of multivariate polynomial equalities and inequalities in the max algebra is equivalent to solving an Extended Linear Complementarity Problem. This allows us to find all solutions of such a system of multivariate polynomial equalities and inequalities and provides a geometrical insight in the structure of the solution set. We also demonst...

We provide a constructive approach to the stratification of the representationand the orbit space of linear actions of compact Lie groups contained in GLn(R) on R n and we show that any d-dimensional stratum, respectively, its closure can be described by d sharp, respectively, relaxed polynomial inequalities and that d is also a lower bound for both cases. Strata of the representation space are...

We consider the problem of enumerating all minimal integer solutions of a monotone system of linear inequalities. We first show that for any monotone system of r linear inequalities in n variables, the number of maximal infeasible integer vectors is at most rn times the number of minimal integer solutions to the system. This bound is accurate up to a polylog(r) factor and leads to a polynomial-...

This work is concerned with the development of inverse-type inequalities for piecewise polynomial functions and, in particular, functions belonging to hp-finite element spaces. The cases of positive and negative Sobolev norms are considered for both continuous and discontinuous finite element functions.The inequalities are explicit both in the local polynomial degree and the local mesh size.The...

Recently Cherchye et al. (2011) reformulated the Walrasian equilibrium inequalities, introduced by Brown and Matzkin (1996), as an integer programming problem and proved that solving the Walrasian equilibrium inequalities is NP-hard. Following Brown and Shannon (2000), we reformulate the Walrasian equilibrium inequalities as the dual Walrasian equilibrium inequalities. Brown and Shannon proved ...

We revisit the facial structure of the axial 3-index assignment polytope. After reviewing known classes of facet-defining inequalities, we present a new class of valid inequalities, and show that they define facets of this polytope. This answers a question posed by Qi and Sun [21]. Moreover, we show that we can separate these inequalities in polynomial time. Finally, we assess the computational...

The trust-region subproblem minimizes a general quadratic function over an ellipsoid and can be solved in polynomial time using a semidefinite-programming (SDP) relaxation. Intersecting the feasible set with a second ellipsoid results in the two-trust-region subproblem (TTRS). Even though TTRS can also be solved in polynomial-time, existing algorithms do not use SDP. In this paper, we investiga...

This paper introduces to constructing problems of convex relaxations for nonconvex polynomial optimization problems. Branch-and-bound algorithms are convex relaxation based. The convex envelopes are of primary importance since they represent the uniformly best convex underestimators for nonconvex polynomials over some region. The reformulationlinearization technique (RLT) generates LP (linear p...

In this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of CN . As a corollary, we present multi-dimensional generalizations of an important result of Coman and Poletsky on Bernstein type inequalities on transcendental curves in C2. 1. Formulation of Main Results 1.1. In this paper we establish some general results on restrictions of...