Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

Categories Constrained Nonlinear Optimization Tags , , ,

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

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

Categories Convex Optimization Tags , , , , ,

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

Development and Calibration of Currency Market Strategies by Global Optimization

Categories Finance and Economics, Global Optimization Applications, Optimization Software and Modeling Systems

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

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

Categories Game Theory, Linear Programming Tags , , , , ,

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

On the implementation and usage of SDPT3 — a Matlab software package for semidefinite-quadratic-linear programming, version 4.0

Categories Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems

This software is designed to solve primal and dual semidefinite-quadratic-linear conic programming problems (known as SQLP problems) whose constraint cone is a product of semidefinite cones, second-order cones, nonnegative orthants and Euclidean spaces, and whose objective function is the sum of linear functions and log-barrier terms associated with the constraint cones. This includes the special … Read more

A relaxed constant positive linear dependence constraint qualification and applications

Categories Constrained Nonlinear Optimization Tags , ,

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification from Minchenko and Stakhovski that was called RCR. We show that RCPLD is enough to ensure the convergence of an … Read more

On mixed-integer sets with two integer variables

Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , ,

We show that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with two integer variables is a crooked cross cut (which we defined recently in another paper). We then extend this observation to show that crooked cross cuts give the convex hull of mixed-integer sets with more integer variables provided that … Read more

On the Use of Stochastic Hessian Information in Unconstrained Optimization

Categories Nonlinear Optimization, Stochastic Programming Tags , ,

This paper describes how to incorporate stochastic curvature information in a Newton- CG method and in a limited memory quasi-Newton method for large scale optimization. The motivation for this work stems from statistical learning and stochastic optimization applications in which the objective function is the sum of a very large number of loss terms, and … Read more

Symmetry-exploiting cuts for a class of mixed-0/1 second order cone programs

Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

We will analyze mixed 0/1 second order cone programs where the fractional and binary variables are solely coupled via the conic constraints. For this special type of mixed-integer second order cone programs we devise a cutting-plane framework based on the generalized Benders cut and an implicit Sherali-Adams reformulation. We show that the resulting cuts are … Read more

Beyond symmetric Broyden for updating quadratic models in minimization without derivatives

Categories Unconstrained Optimization

Some highly successful algorithms for unconstrained minimization without derivatives construct changes to the variables by applying trust region methods to quadratic approximations to the objective function F(x), x in R^n. A quadratic model has (n+1)(n+2)/2 independent parameters, but each new model may interpolate only 2n+1 values of F, for instance. The symmetric Broyden method takes … Read more