In this paper, we suggest an algorithm for price adjustment towards a partial market equilibrium. Its convergence properties are crucially based on Convex Analysis. Our price adjustment corresponds to a subgradient scheme for minimizing a special nonsmooth convex function. This function is the...

Markov-switching models are usually specified under the assumption that all the parameters change when a regime switch occurs. Relaxing this hypothesis and being able to detect which parameters evolve over time is relevant for interpreting the changes in the dynamics of the series, for...

We provide Frank-Wolfe (= Conditional Gradients) method with a convergence analysis allowing to approach a primal-dual solution of convex optimization problem with composite objective function. Additional properties of complementary part of the objective (strong convexity) significantly...

The exact nonnegative matrix factorization (exact NMF) problem is the following: given an m-by-n nonnegative matrix X and a factorization rank r, find, if possible, an m-by-r nonnegative matrix W and an r-by-n nonnegative matrix H such that X = WH. In this paper, we propose two heuristics for...

We solve two related extremal problems in the theory of permutations. A set Q of permutations of the integers 1 to n is inversion-complete (resp., pair-complete) if for every inversion (j, i), where 1 <= i < j <= n, (resp., for every pair (i, j), where i not= j) there exists a permutation in Q where j is before i. It is minimally inversion-complete if in addition no proper subset of Q is inversion-complete; and similarly for paircompleteness. The problems we consider are to determine the maximum cardinality of a minimal inversion-complete set of permutations, and that of a minimal pair-complete set of permutations. The latter problem arises in the determination of the Carathéodory numbers for certain abstract convexity structures on the (n - 1)-dimensional real and integer vector spaces. Using Mantel's Theorem on the maximum number of edges in a triangle-free graph, we determine these two maximum cardinalities and we present a complete description of the optimal sets of permutations for each problem. Perhaps surprisingly (since there are twice as many pairs to cover as inversions), these two maximum cardinalities coincide whenever n >= 4.

We propose a new class of multidimensional poverty indices. To aggregate and weight the different dimensions of poverty, we rely on the preferences of the concerned agents rather than on an arbitrary weighting scheme selected by the analyst. The Pareto principle is, therefore, satisfied among...

Recent extensions of the standard Dixit-Stiglitz (1977) model, that go beyond the CES sub-utility assumption, while maintaining monopolistic competition, have mainly emphasized the role of iintrasectoral substitutability. We argue that introducing oligopolistic competition can be an alternative...

The achievements and limitations of the classical theory of optimal labor-income taxation based on social welfare functions are now well known, although utilitarianism still dominates public economics. We review the recent interest that has arisen for broadening the normative approach and making...

We consider multiobjective and parametric versions of the global minimum cut problem in undirected graphs and bounded-rank hypergraphs with multiple edge cost functions. For a fixed number of edge cost functions, we show that the total number of supported non-dominated (SND) cuts is bounded by a...

Expanding variety and the number of offered products is attractive for a firm to fit customer needs. Nevertheless, the greater complexity and the proliferation of stock-keeping units (SKUs) without substantial differentiation may not substantially improve customer satisfaction while raising...