A5022592293- Advanced Optimization Algorithms Research
- Optimization and Variational Analysis
- Sparse and Compressive Sensing Techniques
- Iterative Methods for Nonlinear Equations
- Differential Equations and Numerical Methods
- Advanced Control Systems Optimization
- Mathematics and Applications
- Advanced Numerical Methods in Computational Mathematics
Universidade de São Paulo
2019-2023
Sequential optimality conditions play a major role in proving stronger global convergence results of numerical algorithms for nonlinear programming. Several extensions are described conic contexts, which many open questions have arisen. In this paper, we present new sequential the context general framework, explains and improves several known specific cases, such as semidefinite programming, second-order cone particular, show that feasible limit points sequences generated by augmented...
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type from programming. As an application these conditions, we provide a unified global convergence proof class algorithms to stationary points without assuming neither uniqueness Lagrange multiplier nor boundedness multipliers set. This algorithm includes, instance, general forms augmented Lagrangian, sequential quadratic programming, and interior point methods....
In a previous paper [R. Andreani, G. Haeser, L. M. Mito, H. Ram\'irez, T. P. Silveira. First- and second-order optimality conditions for cone semidefinite programming under constant rank condition. Mathematical Programming, 2023. DOI: 10.1007/s10107-023-01942-8] we introduced constraint qualification nonlinear by considering all faces of the underlying cone. This condition is independent Robinson's it implies strong necessary which depends on single Lagrange multiplier instead full set...
The constraint nondegeneracy condition is one of the most relevant and useful qualifications in nonlinear semidefinite programming. It can be characterized terms any fixed orthonormal basis the, let us say, $\ell$-dimensional kernel matrix, by linear independence a set $\ell(\ell+1)/2$ derivative vectors. We show that this requirement equivalently formulated smaller set, $\ell$ vectors, considering all bases instead. This allows to identify not are for qualification defined, giving rise...
The well known constant rank constraint qualification [Math. Program. Study 21:110--126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic context exploiting the eigenvector structure of problem. In this paper we propose more general and geometric approach defining new extension condition context. main advantage our is that are able recast strong second-order properties in particular, obtain necessary optimality stronger than classical one obtained...
The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used sensitivity analysis, global convergence of first- and second-order algorithms, computing the derivative value function. In this paper we discuss naive extensions rank-type qualifications to cone programming semidefinite which are based on Approximate-Karush-Kuhn-Tucker necessary optimality condition application reduction approach. Our definitions strictly weaker than...
Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built under nondegeneracy and strict complementarity. In this paper we establish condition of such type two classes problems, namely semidefinite second-order cone programming, assuming Robinson's constraint qualification weak constant rank-type property which are, together, strictly weaker than nondegeneracy. Our approach is done via penalty-based...
In [R. Andreani, G. Haeser, L. M. Mito, H. Ram\'irez C., Weak notions of nondegeneracy in nonlinear semidefinite programming, arXiv:2012.14810, 2020] the classical notion (or transversality) and Robinson's constraint qualification have been revisited context programming exploiting structure problem, namely, its eigendecomposition. This allows formulating conditions equivalently terms (positive) linear independence significantly smaller sets vectors. this paper we extend these ideas to...