References in periodicals archive

The topics include the maximal monotonicity of the sum of a maximal monotone linear relation and the subdifferential operator of a sublinear function, sharing risk and resources, descent methods for mixed variational inequalities with non-smooth mappings, strategic behavior in multiple-period financial markets, and towards using coderivatives for convergence rates in regularization.

Optimization theory and related topics; proceedings

Another generalization of an invex function is an F-convex function which is defined in terms of a sublinear function, that is, a function that is subadditive and positively homogeneous.

The function F is called (strictly) (F, b, [phi], [rho], [theta])-univex at [x.sup.*] if there exist functions b: X x X [right arrow] [R.sub.+] \{0} [equivalent to] (0, [infinity]),[phi]: R [right arrow] R, [rho]: X x X [right arrow] R, and [theta]: X x X [right arrow] [R.sup.n], and a sublinear function F(x, [x.sup.*]; *): [R.sup.n] [right arrow] R such that for each x [member of] X(x = [x.sup.*]),

The function F is said to be (strictly) (F, b, [phi], [rho], [theta])-pseudounivex at [x.sup.*] if there exist functions b: X x X [right arrow] [R.sub.+]\{0} = (0, oc),[phi]: R [right arrow] R,[rho]: X x X [right arrow] R, and [theta]: X x X [right arrow] [R.sup.n], and a sublinear function F(x,[x.sup.*]; *): [R.sup.n] [right arrow] R such that for each x [member of] X(x [not equal to] [x.sup.*]),

The function F is said to be (prestrictly)(F, b, [phi], [rho], [theta])-quasiunivex at [x.sup.*] if there exist functions b: X x X [right arrow] [R.sub.+]\{0}[equivalent to] (0, [infinity]),[phi]: R [right arrow] R, [rho]: X x X [right arrow] R, and [theta]: X x X [right arrow] [R.sup.n], and a sublinear function F(x, [x.sup.*]; *): [R.sup.n] [right arrow] R such that for each x [member of] X,

F is said to be (F, b, [phi], [rho], [theta])-quasiunivex at [x.sup.*] if there exist functions b: X x X [right arrow] [R.sub.+]\{0} [equivalent to] (0, [infinity]), [phi]: R [right arrow] R, [rho]: X x X [right arrow] R, and 0: X x X - [R.sup.n], and a sublinear function F(x, [x.sup.*]; *): [R.sup.n] [right arrow] R such that for each x [member of] X,

Optimality conditions and duality in minmax fractional programming, part I: necessary and sufficient optimality conditions

Similarly, sublinear functions will produce good correspondence on most data points at the expense of some larger errors.

Parameter Estimation in Ordinary Differential Equations Modeling via Particle Swarm Optimization