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In this paper we obtain second- and first-order optimality conditions of Kuhn-Tucker type and Fritz John one for weak efficiency in the vector problem with inequality constraints. In the necessary conditions we suppose that the objective…
We propose a method for solving Karush-Kuhn-Tucker (KKT) systems that exploits block triangular submatrices by first using a Schur complement decomposition to isolate the block triangular submatrices then performing a block backsolve where…
Distribution network reconfiguration (DNR) is an effective approach for optimizing distribution network operation. However, the DNR problem is computationally challenging due to the mixed-integer non-convex nature. One feasible approach for…
In this paper, we derive optimality results for greedy Bayesian-network search algorithms that perform single-edge modifications at each step and use asymptotically consistent scoring criteria. Our results extend those of Meek (1997) and…
Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…
Quadratic programmingis a class of constrained optimization problem with quadratic objective functions and linear constraints. It has applications in many areas and is also used to solve nonlinear optimization problems. This article focuses…
We revisit the structure learning problem for dynamic Bayesian networks and propose a method that simultaneously estimates contemporaneous (intra-slice) and time-lagged (inter-slice) relationships between variables in a time-series. Our…
The search space of Bayesian Network structures is usually defined as Acyclic Directed Graphs (DAGs) and the search is done by local transformations of DAGs. But the space of Bayesian Networks is ordered by DAG Markov model inclusion and it…
This paper proposes and evaluates the k-greedy equivalence search algorithm (KES) for learning Bayesian networks (BNs) from complete data. The main characteristic of KES is that it allows a trade-off between greediness and randomness, thus…
Gradient-flow (GF) viewpoints unify and illuminate optimization algorithms, yet most GF analyses focus on unconstrained settings. We develop a geometry-respecting framework for constrained problems by (i) reparameterizing feasible sets with…
Most numerical methods developed for solving nonlinear programming problems are designed to find points that satisfy certain optimality conditions. While the Karush-Kuhn-Tucker conditions are well-known, they become invalid when constraint…
Some necessary and sufficient optimality conditions for inequality constrained problems with continuously differentiable data were obtained in the papers [I. Ginchev and V.I. Ivanov, Second-order optimality conditions for problems with…
We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any…
We propose a hierarchical training algorithm for standard feed-forward neural networks that adaptively extends the network architecture as soon as the optimization reaches a stationary point. By solving small (low-dimensional) optimization…
In this paper, we study second-order necessary and sufficient optimality conditions of Karush--Kuhn--Tucker-type for locally optimal solutions in the sense of Pareto to a class of multi-objective optimal control problems with mixed…
Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing…
This paper is devoted to studying the stability properties of the Karush-Kuhn-Tucker (KKT) solution mapping $S_{\rm KKT}$ for Nash equilibrium problems (NEPs) with canonical perturbations. Firstly, we obtain an exact characterization of the…
In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak…
Knowledge Tracing (KT), tracking a human's knowledge acquisition, is a central component in online learning and AI in Education. In this paper, we present a simple, yet effective strategy to improve the generalization ability of KT models:…
Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…