Abstract We consider primal-dual pairs of semidefinite programs and assume that they are singular, i.e., both primal dual either weakly feasible or infeasible. Under such circumstances, strong duality may break down the might have a nonzero gap. Nevertheless, there arbitrary small perturbations to problem data which would make them strongly thus zeroing In this paper, we conduct an asymptotic a...

A recent trend in probabilistic inference emphasizes the codification of models in a formal syntax, with suitable high-level features such as individuals, relations, and connectives, enabling descriptive clarity, succinctness and circumventing the need for the modeler to engineer a custom solver. Unfortunately, bringing these linguistic and pragmatic benefits to numerical optimization has prove...

In this paper we present a redesign of a linear algebra kernel of an interior point method to avoid the explicit use of problem matrices. The only access to the original problem data needed are the matrix-vector multiplications with the Hessian and Jacobian matrices. Such a redesign requires the use of suitably preconditioned iterative methods and imposes restrictions on the way the preconditio...

We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of arithmetic operations and the finest precision required are exhibited.

This paper considers the problem of Bayesian optimization for systems with safety-critical constraints, where both objective function and constraints are unknown, but can be observed by querying system. In applications, system at an infeasible point have catastrophic consequences. Such require a safe learning framework, such that performance optimized while satisfying high probability. this we ...

Most existing interior-point methods for a linear complementarity problem (LCP) require the existence of a strictly feasible point to guarantee that the iterates are bounded. Based on a regularized central path, we present an infeasible interior-point algorithm for LCPs without requiring the strict feasibility condition. The iterates generated by the algorithm are bounded when the problem is a ...

We propose an infeasible interior proximal method for solving variational inequality problems with maximal monotone operators and linear constraints. The interior proximal method proposed by Auslender, Teboulle and Ben-Tiba [3] is a proximal method using a distance-like barrier function and it has a global convergence property under mild assumptions. However, this method is applicable only to p...

The development of algorithms for semide nite programming is an active research area, based on extensions of interior point methods for linear programming. As semide nite programming duality theory is weaker than that of linear programming, only partial information can be obtained in some cases of infeasibility, nonzero optimal duality gaps, etc. Infeasible start algorithms have been proposed w...