We study the use of black-box LDL factorizations for solving the augmented systems (KKT systems) associated with least-squares problems and barrier methods for linear programming (LP). With judicious regularization parameters, stability can be achieved for arbitrary data and arbitrary permutations of the KKT matrix. This offers improved efficiency compared to implementations based on “pure norm...

In this paper, we establish second-order KKT conditions of a set-valued optimization problem and study Mond-Weir, Wolfe, mixed types duals with the help contingent epiderivative generalized cone convexity assumptions.

Operative planning in gas networks with prescribed binary decisions yields large scale nonlinear programs defined on graphs. We study the structure of the KKT systems arising in interior methods and present a customized direct solution algorithm. Computational results indicate that the algorithm is suitable for optimization in small and medium-sized gas networks.

In the first part of the tutorial, we introduced the problem of unconstrained optimization, provided necessary and sufficient conditions for optimality of a solution to this problem, and described the gradient descent method for finding a (locally) optimal solution to a given unconstrained optimization problem. We now describe another method for unconstrained optimization, namely Newton’s metho...

Convex optimization solvers are widely used in the embedded systems that require sophisticated algorithms including model predictive control (MPC). In this paper, we aim to reduce online solve time of such convex so as total runtime algorithm and make it suitable for real-time optimization. We exploit property Karush–Kuhn–Tucker (KKT) matrix involved solution problem only some parts change duri...

We address the problem of self-supervised learning for predicting shape supporting terrain (i.e. which will provide rigid support robot during its traversal) from sparse input measurements. The method exploits two types ground-truth labels: dense 2.5D maps and poses, both estimated by a usual SLAM procedure offline recorded show that poses are required because straightforward supervised 3D only...

In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the function is achieved using auxiliary linear program that leads to a bilevel program, which provides lower bound original problem. The reduced single level formulation with help Karush–Kuhn–Tucker (KKT) conditions. Incorporating KKT conditions lead comple...