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Multicriterion optimization and Pareto optimality are fundamental tools in economics. In this paper we propose a new relaxation method for solving multiple objective quadratic programming problems. Exploiting the technique of the linear…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
We study the properties of secret sharing schemes, where a random secret value is transformed into shares distributed among several participants in such a way that only the qualified groups of participants can recover the secret value. We…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of four algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been…
We consider the problem of computing an equilibrium in a class of \textit{nonlinear generalized Nash equilibrium problems (NGNEPs)} in which the strategy sets for each player are defined by equality and inequality constraints that may…
We propose FlexQP, an always-feasible convex quadratic programming (QP) solver based on an $\ell_1$ elastic relaxation of the QP constraints. If the original constraints are feasible, FlexQP provably recovers the optimal solution. If the…
In this paper, the discrete-time modified algebraic Riccati equation (MARE) is solved when the system model is completely unavailable. To achieve this, firstly a brand new iterative method based on the standard discrete-time algebraic…
This article proposes a new class of general linear method with $p=q$ and $r=s=p+1$. The construction of the present method is carried out using order conditions and error minimization subject to $A$- stability constraints. The proposed…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
This paper presents a stabilized sequential quadratic programming (SQP) method for solving optimization problems in Banach spaces. The optimization problem considered in this study has a general form that enables us to represent various…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
In this paper we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration and jerk constraints. Such a problem arises in industrial contexts such as automated…
This paper investigates the performance of Newton's method, iterative Linear Quadratic Regulator (iLQR), and Differential Dynamic Programming (DDP) in solving discrete-time optimal control problems. We offer a unified perspective on these…
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…
LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…
Solving Quadratic equation is one of the intrinsic interests as it is the simplest nonlinear equations. A novel approach for solving Quadratic Equation based on Genetic Algorithms (GAs) is presented. Genetic Algorithms (GAs) are a technique…