Based on minimizing a piecewise diierentiable lp function subject to a single inequality constraint, this paper discusses algorithms for a discretized regularization problem for ill-posed inverse problems. We examine computational challenges of solving this regularization problem. Possible minimization algorithms such as the steepest descent method, iteratively weighted least squares (IRLS) met...

Consider the minimization problem with a convex separable objective function over a feasible region defined by linear equality constraint(s)/linear inequality constraint of the form “greater than or equal to” and bounds on the variables. A necessary and sufficient condition and a sufficient condition are proved for a feasible solution to be an optimal solution to these two problems, respectivel...

In an earlier paper we have shown, how one can successfully use constraint satisfaction techniques for proving and solving formulae in the first-order predicate language over the reals (i.e., real first-order constraints). This approach was restricted to inputs that contain inequality symbols such as ≤, but no equality symbols (=) or disequality symbols ( 6=). In this paper we lay the basis for...

Vector quantization is an eecient compression technique for which many variants are known. Product code vector quantizers use multiple codebooks for coding separately features of a vector. In shape-gain and mean-shape-gain vector quantizers, the bottleneck in the encoder is a nearest neighbor search on a hypersphere. We deene an angular constraint for speeding up the search in shape-gain and me...

Many applications of static analysis and verification compute on some abstract domain based on convex polyhedra. Traditionally, most of these applications are restricted to convex polyhedra that are topologically closed. When adopting the Double Description (DD) method [8], a closed convex polyhedron can be specified in two ways, using a constraint system or a generator system: the constraint s...

In this paper we propose a new criterion for solving the problem of channel shortening in multi-carrier systems. In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Minimum mean square error (MMSE) method for TEQ does not give satisfactory results. In [1] a new criterion for ...

This work pertains to the Knuth-Bendix (KB) algorithm which tries to find a complete set of reductions from a given set of equations. In the KB algorithm a term ordering is employed and it is required that every equation be orientable in the sense that the left-hand side be greater than the right. The KB algorithm halts if a nonorientable equation is produced. A generalization of the KB algorit...

Structural topology optimization problems have been traditionally stated and solved by means of maximum stiffness formulations. On the other hand, some effort has been devoted to stating and solving this kind of problems by means of minimum weight formulations with stress (and/or displacement) constraints. It seems clear that the latter approach is closer to the engineering point of view, but i...

We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. This class of problems includes the Yamabe problem and the Einstein constraint equations, which simultaneously contain several challenging features: high spatial dimension n > 3, varying (potentially non-smoot...

The celebrated Farkas lemma originated in Farkas (1902) provides us an attractively simple and extremely useful characterization for a linear inequality to be a consequence of a linear inequality system on the Euclidean space Rn . This lemma has been extensively studied and extended in many directions, including conic systems (linear, sublinear, convex), infinite/semi-infinite convex inequality...