6 Spectral Graph Theory 16 6.1 Graph Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 6.2 Polynomial interlacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6.2.1 An Application to Expander Graphs . . . . . . . . . . . . . . . . . . 18 6.3 Connectivity as a Minimization Problem . . . . . . . . . . . . . . . . . . . . 20 6.4 Courant-Fisher and Alg...

In this paper we study optimization problems with equality and inequality constraints on a Banach space where the objective function and the binding constraints are either differentiable at the optimal solution or Lipschitz near the optimal solution. Necessary and sufficient optimality conditions and constraint qualifications in terms of the Michel–Penot subdifferential are given, and the resul...

In this paper, the problem of coordinated motion control of a nonholonomic mobile platform with a serial manipulator mounted on top of the platform is addressed. The redundancy resolution algorithm bases on a constraint optimization approach, where the non–holonomic behaviour of the platform is modeled into inequality constraints leading to a convex optimization problem.

Optimization problems with complementarity constraints are closely related to optimization problems with variational inequality constraints and bilevel programming problems. In this paper, under mild constraint qualifications, we derive some necessary and sufficient optimality conditions involving the proximal coderivatives. As an illustration of applications, the result is applied to the bilev...

The foot-mounted inertial navigation system is an important method of pedestrian navigation as it, in principle, does not rely any external assistance. A real-time range decomposition constraint method is proposed in this paper to combine the information of dual foot-mounted inertial navigation systems. It is well known that low-cost inertial pedestrian navigation aided with both ZUPT (zero vel...

A state-space characterization is given for strongly strict negative-imaginary systems. It facilitates both robust analysis and synthesis methods for interconnected negative-imaginary systems. Numerical advantages are achieved by avoiding a non-convex rank constraint, a non-strict inequality condition and a minimality assumption present in previous literature.

We deal with differential conditions for local optimality. The conditions we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based only on first and second order derivatives. A similar result is proved for equality constrained problems, although necessary conditions require regularity of the equality constraints.

In this paper, a method is suggested to solve the nonlinear interval number programming problem with uncertain coefficients both in nonlinear objective function and nonlinear constraints. Based on an order relation of interval number, the uncertain objective function is transformed into two deterministic objective functions, in which the robustness of design is considered. Through a modified po...

A simple interval method is suggested for globally solving optimization problems of the following type: minimize the objective function φo(x) subject to the functional constraints φo(x) ≤ 0, i=1,...r and the boundary constraints x∈ X(o) where x is a n-dimensional vector and X(o) is a given initial search region (a box). All the functions involved are assumed continuously differentiable in X(o)....

One of the problems with the traditional nite domains approach to solving integer problems in a constraint logic programming context is that all variables require explicit bounds. If no explicit bounds are available then the nite domain solver can be very ineecient on certain classes of problem. We present an alternative approach to solving integer constraints based on a polynomial-time solver ...