Coverings and Matchings in r-Partite Hypergraphs

Ryser’s conjecture postulates that, for $r$-partite hypergraphs, $\tau \leq (r-1) \nu$ where $\tau$ is the covering number of the hypergraph and $\nu$ is the matching number. Although this conjecture has been open since the 1960s, researchers have resolved it for special cases such as for intersecting hypergraphs where $r \leq 5$. In this paper, we … Read more

A splitting method for separate convex programming with linking linear constraints

We consider the separate convex programming problem with linking linear constraints, where the objective function is in the form of the sum of m individual functions without crossed variables. The special case with m=2 has been well studied in the literature and some algorithms are very influential, e.g. the alternating direction method. The research for … Read more

Approximating the Least Core Value and Least Core of Cooperative Games with Supermodular Costs

We study the approximation of the least core value and the least core of supermodular cost cooperative games. We provide a framework for approximation based on oracles that approximately determine maximally violated constraints. This framework yields a (3 + \epsilon)-approximation algorithm for computing the least core value of supermodular cost cooperative games, and a polynomial-time … Read more

A Faster Algorithm for Quasi-convex Integer Polynomial Optimization

We present a faster exponential-time algorithm for integer optimization over quasi-convex polynomials. We study the minimization of a quasi-convex polynomial subject to s quasi-convex polynomial constraints and integrality constraints for all variables. The new algorithm is an improvement upon the best known algorithm due to Heinz (Journal of Complexity, 2005). A lower time complexity is … Read more

Derivative-free methods for nonlinear programming with general lower-level constraints

Augmented Lagrangian methods for derivative-free continuous optimization with constraints are introduced in this paper. The algorithms inherit the convergence results obtained by Andreani, Birgin, Martínez and Schuverdt for the case in which analytic derivatives exist and are available. In particular, feasible limit points satisfy KKT conditions under the Constant Positive Linear Dependence (CPLD) constraint qualification. … Read more

Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore, the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated in usual convergence theories. However, … Read more

A Penalty-Interior-Point Algorithm for Nonlinear Constrained Optimization

Penalty and interior-point methods for nonlinear optimization problems have enjoyed great successes for decades. Penalty methods have proved to be effective for a variety of problem classes due to their regularization effects on the constraints. They have also been shown to allow for rapid infeasibility detection. Interior-point methods have become the workhorse in large-scale optimization … Read more

Alternating proximal algorithms for constrained variational inequalities. Application to domain decomposition for PDE’s

Let $\cX,\cY,\cZ$ be real Hilbert spaces, let $f : \cX \rightarrow \R\cup\{+\infty\}$, $g : \cY \rightarrow \R\cup\{+\infty\}$ be closed convex functions and let $A : \cX \rightarrow \cZ$, $B : \cY \rightarrow \cZ$ be linear continuous operators. Let us consider the constrained minimization problem $$ \min\{f(x)+g(y):\quad Ax=By\}.\leqno (\cP)$$ Given a sequence $(\gamma_n)$ which tends toward … Read more

On the Equivalencey of Linear Programming Problems and Zero-Sum Games

In 1951, Dantzig showed the equivalence of linear programming and two-person zero-sum games. However, in the description of his reduction from linear programming to zero-sum games, he noted that there was one case in which his reduction does not work. This also led to incomplete proofs of the relationship between the Minmax Theorem of game … Read more

Development and Calibration of Currency Market Strategies by Global Optimization

We have developed a new financial indicator – called the Interest Rate Differential Adjusted for Volatility (IRDAV) measure – to assist investors in currency markets. On a monthly basis, we rank currency pairs according to this measure and generate a basket of pairs with the highest IRDAV values. Under positive market conditions, an IRDAV based … Read more