In this paper a noncooperative, two person, zero sum, stochastic differential game is formulated and solved that is described by a linear stochastic system and a quadratic cost functional for the two players. The optimal strategies for the two players are given explicitly using a relatively simple direct method. The noise process for the two player linear system can be an arbitrary square integ...

In this paper, a novel method is introduced to design Nyquist filters with prescribed inter symbol interference (ISI) energy. The computation is based on the iterative weighted least-squares optimization with a quadratic constraint. The weighted stop band and the tail energies of the Nyquist filter are minimized iteratively while the quadratic constraint prescribing the ISI energy is enforced. ...

In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of smooth and nonsmooth function. The proposed deals with unconstrained convex problems. This free from any kind priori chosen parameters or ordering information functions. At every iteration method...

Abstract We prove a quadratic sparse domination result for general non-integral square functions S . That is, $$p_0 \in [1,2)$$ p 0 ∈ [ 1 , 2 ) a...

When we solve an ordinary nonlinear programming problem by the most and popular sequential quadratic programming (SQP) method, one of the difficulties that we must overcome is to ensure the consistence of its QP subproblems. In this paper, we develop a new SQP method which can assure that the QP subproblem at every iteration is consistent. One of the main techniques used in our method involves ...

11.1 Prime fields of odd characteristic 201 Representations and reductions • Multiplication • Inversion and division • Exponentiation • Squares and square roots 11.2 Finite fields of characteristic 2 213 Representation • Multiplication • Squaring • Inversion and division • Exponentiation • Square roots and quadratic equations 11.3 Optimal extension fields 229 Introduction • Multiplication • Exp...

in this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. first we introduce a parametric equivalent of the problem. then a bisection and a generalized newton-based method algorithms are presented to solve it. in order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

Next, we claim that x ∈ Qp is a square if and only if x = py for n ∈ Z, and y ∈ Zp a padic unit. One direction is obvious. The second direction is also fairly obvious–just refer to the previous case, and also note that p is itself NOT a square in Qp (since if it had a square root, then that square root would have valuation 12 ). We can conclude then that [ Qp : Q×2 p ] = 4, and is given by {1, ...