The quadratic minimum spanning tree problem is to find a spanning tree on a graph that minimizes a quadratic objective function of the edge weights. In this paper, the quadratic minimum spanning tree problem is concerned on the graph with edge weights being assumed as uncertain variables. The notion of the uncertain quadratic -minimum spanning tree is introduced by using the uncertain chance co...

We present a general semidefinite relaxation scheme for general n-variate quartic polynomial optimization under homogeneous quadratic constraints. Unlike the existing sum-of-squares (SOS) approach which relaxes the quartic optimization problems to a sequence of (typically large) linear semidefinite programs (SDP), our relaxation scheme leads to a (possibly nonconvex) quadratic optimization prob...

QP is the optimization of a quadratic function subject to linear equality and inequality constraints. It arises in multiple objective decision making where the departure of the actual decisions from their corresponding ideal, or bliss, value can be evaluated using a weighted quadratic norm as a measure of deviation. The formulation of mean-variance optimization of uncertain systems also leads t...

In this paper we provide a second order analysis for strong solutions in the optimal control of parabolic equations. We consider the case of box constraints on the control and final integral constraints on the state. In contrast to sufficient conditions assuring quadratic growth in the weak sense, i.e. when the cost increases at least quadratically for admissible controls uniformly near to the ...

Abstract Bezier is one of the influent polynomial and important tool for interpolation because it is easy to compute and is also very stable. In this paper, we develop very simpler constraints for Quadratic and Cubic Bezier curve which they ensure to constrained by a line. The end control points of the Quadratic and Cubic Bezier curve will be left on user desire and only middle control points o...

An algorithm for solving quadratic, two-stage stochastic problems is developed. The algorithm is based on the framework of the Branch and Fix Coordination (BFC) method. These problems have continuous and binary variables in the first stage and only continuous variables in the second one. The objective function is quadratic and the constraints are linear. The nonanticipativity constraints are fu...

Estimation of time-varying regression model constrained at each time moment by linear inequalities is a natural statistical formulation of a wide class of nonstationary signal processing problems. The presence of linear constraints turns the originally quadratic three-diagonal problem of minimizing the residual squares sum, which is solvable by the linear Kalman-Bucy filtration-smoothing proced...

Optimal power flow (OPF) over power transmission networks poses challenging large-scale nonlinear optimization problems, which involve a large number of quadratic equality and indefinite quadratic inequality constraints. These computationally intractable constraints are often expressed by linear constraints plus matrix additional rank-one constraints on the outer products of the voltage vectors...

We propose a sequential quadratic programming (SQP) method for the optimal control of large-scale dynamical systems. The method uses modified multiple shooting to discretize the dynamical constraints. When these systems have relatively few parameters, the computational complexity of the modified method is much less than that of standard multiple shooting. Moreover, the proposed method is demons...