Most existing interior-point methods for a linear complementarity problem (LCP) require the existence of a strictly feasible point to guarantee that the iterates are bounded. Based on a regularized central path, we present an infeasible interior-point algorithm for LCPs without requiring the strict feasibility condition. The iterates generated by the algorithm are bounded when the problem is a ...

Rationality is a fundamental concept in economics. Most researchers will accept that human beings are not fully rational. Herbert Simon suggested that we are “bounded rational”. However, it is very difficult to quantify “bounded rationality”, and therefore it is difficult to pinpoint its impact to all those economic theories that depend on the assumption of full rationality. Ariel Rubinstein pr...

Assume that point evaluation is a bounded functional on H for each point z ∈ C, and also that H has the following symmetry property: H is closed under the operations f(z) 7→ f(z)(z− ζ)/(z− ζ) (provided f(ζ) = 0) and f(z) 7→ f(z). These assumptions ensure that H is a Hilbert space of entire functions in the sense of de Branges [4]. According to de Branges’ theory, there exists an entire function...

The efficient evaluation of multivariate polynomials at many points is an important operation for polynomial system solving. Kedlaya and Umans have recently devised a theoretically algorithm this task when the coefficients are integers or they lie in finite field. In paper, we assume that set where need to evaluate fixed “sufficiently generic”. Under these restrictions, present quasi-optimal mu...

We prove that every bounded type Siegel disk of a rational map must be a quasi-disk with at least one critical point on its boundary. This verifies Douady-Sullivan’s conjecture in the case of bounded type rotation numbers.

The model-checking games associated with fixed-point logics are parity games, and it is currently not known whether the strategy problem for parity games can be solved in polynomial time. We study Solitaire-LFP, a fragment of least fixedpoint logic, whose evaluation games are nested soltaire games. This means that on each strongly connected component of the game, only one player can make nontri...

The paper is an attempt to generalize a methodology [1; 93] and [2, 3; 95], which is similar to the bounded-input bounded-output (BIBO) method currently widely used [4-9] for the system stability studies. The presented in [1, 2] methodology allows decomposition of input space into bounded subspaces and defining for each subspace its bounding surface. It also defines a corresponding predefined c...

Let (f1, . . . , fs) be a polynomial family in Q[X1, . . . , Xn] (with s 6 n− 1) of degree bounded by D. Suppose that 〈f1, . . . , fs〉 generates a radical ideal, and defines a smooth algebraic variety V ⊂ Cn. Consider a projection π : Cn → C. We prove that the degree of the critical locus of π restricted to V is bounded by Ds(D−1)n−s ( n n−s ) . This result is obtained in two steps. First the c...

In this note we study some topological properties of bounded sets and Bourbaki-bounded sets. Also we introduce two types of Bourbaki-bounded homomorphisms on topological groups  including, n$-$Bourbaki-bounded homomorphisms and$hspace{1mm}$ B$-$Bourbaki-bounded homomorphisms. We compare them to each other and with the class of continuous homomorphisms. So, two topologies are presented on them a...

We consider the motion planning problem for a point constrained to move along a smooth closed convex path of bounded curvature. The workspace of the moving point is bounded by a convex polygon with m vertices, containing an obstacle in a form of a simple polygon with n vertices. We present an O(m + n) time algorithm finding the path, going around the obstacle, whose curvature is the smallest po...