Using variational analysis techniques, we study convex-composite optimization problems. In connection with such a problem, we introduce several new notions as variances of the classical KKT conditions. These notions are shown to be closely related to the notions of sharp or weak sharp solutions. As applications, we extend some results on metric regularity of inequalities from the convex case to...

Prediction of wave-induced instantaneous (oscillatory or momentary) liquefaction is particularly important for the design offshore foundations. Most previous studies applied linear Darcy model to characterize porous flow in a seabed. This treatment was found cause fallacious tensile stresses non-cohesive In this study, overcome such shortcomings models, non-Darcy proposed based on Karush–Kuhn–T...

We consider a special class of optimization problems that we call Mathematical Programs with Vanishing Constraints, MPVC for short, which serves as a unified framework for several applications in structural and topology optimization. Since an MPVC most often violates stronger standard constraint qualification, first-order necessary optimality conditions, weaker than the standard KKT-conditions,...

We present several embedding results for 3-graded Lie algebras and KKT algebras that are generated by two homogeneous elements of degrees 1 and −1. We also propose the canonical kernel function for a “universal Bergman kernel” which extends the usual Bergman kernel on a bounded symmetric domain to a group-valued function or, in terms of formal series, to an element in the formal completion of t...

This paper is aimed toward the definition of a new exact augmented Lagrangian function for two-sided inequality constrained problems. The distinguishing feature of this augmented Lagrangian function is that it employs only one multiplier for each two-sided constraint. We prove that stationary points, local minimizers and global minimizers of the exact augmented Lagrangian function correspond ex...

to obtain an approximate second-order KKT solution of the `p-norm models in polynomial time with a fixed error tolerance, and then test our `p-norm models on CRSP(1992-2013) and also S&P 500 (2008-2012) data. The empirical results illustrate that our `p-norm regularized models can generate portfolios of any desired sparsity with portfolio variance, portfolio return and Sharpe Ratio comparable t...

We address the iterative solution of KKT systems arising in the solution of convex quadratic programming problems. Two strictly related and well established formulations for such systems are studied with particular emphasis on the effect of preconditioning strategies on their relation. Constraint and augmented preconditioners are considered, and the choice of the augmentation matrix is discusse...

Nonnegative Matrix Factorization (NMF) can be used to approximate a large nonnegative matrix as a product of two smaller nonnegative matrices. This paper shows in detail how an NMF algorithm based on Newton iteration can be derived utilizing the general Karush-KuhnTucker (KKT) conditions for first-order optimality. This algorithm is suited for parallel execution on shared-memory systems. It was...

We present an interior proximal point method with Bregman distance, whose Bregman function is separable and the zone is the interior of the positive orthant, for solving the quasiconvex optimization problem under nonnegative constraints. We establish that the sequence generated by our algorithm is well defined and we prove convergence to a solution point when the sequence of parameters goes to ...