In the last few decades, the search for exact algorithms for known NP-hard geometric problems has intensified. Many of these solutions make use of Integer Linear Programming (ILP) modeling and rely on state of the art solvers, to be able to find optimal solutions for large instances in a matter of minutes. In this work, … Read more
Typical output from an optimization solver is a single optimal solution. At the same time, a set of high-quality and diverse solutions could be beneficial in a variety of contexts, for example problems involving imperfect information, or those for which the structure of high-quality solution vectors can reveal meaningful insights. In view of this, we … Read more
This article considers the two-player composite Nash equilibrium (CNE) problem with a separable non-smooth part, which is known to include the composite saddle-point (CSP) problem as a special case. Due to its two-block structure, this problem can be solved by any algorithm belonging to the block-decomposition hybrid proximal-extragradient (BD-HPE) framework. The framework consists of a … Read more
Regularized and stabilized sequential quadratic programming methods are two classes of sequential quadratic programming (SQP) methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that provides a strong connection between augmented Lagrangian methods and stabilized SQP methods. The method … Read more
In stochastic optimal control the distribution of the exogenous noise is typically unknown and must be inferred from limited data before dynamic programming (DP)-based solution schemes can be applied. If the conditional expectations in the DP recursions are estimated via kernel regression, however, the historical sample paths enter the solution procedure directly as they determine … Read more
We propose a new gradient method for quadratic programming, named SDC, which alternates some SD iterates with some gradient iterates that use a constant steplength computed through the Yuan formula. The SDC method exploits the asymptotic spectral behaviour of the Yuan steplength to foster a selective elimination of the components of the gradient along the … Read more
Consider the consensus problem of minimizing $f(x)=\sum_{i=1}^n f_i(x)$ where each $f_i$ is only known to one individual agent $i$ out of a connected network of $n$ agents. All the agents shall collaboratively solve this problem and obtain the solution subject to data exchanges restricted to between neighboring agents. Such algorithms avoid the need of a … Read more
Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems in practical time. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a structural sparsity of input SDP by factorizing the variable matrices, and it shrinks the computation time. In this paper, we propose a new factorization based on the … Read more
We propose the bound-optimal cutting plane method. It is a new paradigm for cutting plane generation in Mixed Integer Programming allowing for the simultaneous generation of k cuts which, when added to the current Linear Programming elaxation, yield the largest bound improvement. By Linear Programming duality arguments and standard linearization techniques we show that, for … Read more
In this paper, we analyze the iteration-complexity of a generalized forward-backward (GFB) splitting algorithm, recently proposed in~\cite{gfb2011}, for minimizing the large class of composite objectives $f + \sum_{i=1}^n h_i$ on a Hilbert space, where $f$ has a Lipschitz-continuous gradient and the $h_i$’s are simple (i.e. whose proximity operator is easily computable ). We derive iteration-complexity … Read more