Convergence of the Lasserre Hierarchy of SDP Relaxations for Convex Polynomial Programs without Compactness

The Lasserre hierarchy of semidefinite programming (SDP) relaxations is an effective scheme for finding computationally feasible SDP approximations of polynomial optimization over compact semi-algebraic sets. In this paper, we show that, for convex polynomial optimization, the Lasserre hierarchy with a slightly extended quadratic module always converges asymptotically even in the face of non-compact semi-algebraic feasible sets. We do this by exploiting a coercivity property of convex polynomials that are bounded below. We further establish that the positive definiteness of the Hessian of the associated Lagrangian at a saddle-point (rather than the objective function at each minimizer) guarantees finite convergence of the hierarchy. We obtain finite convergence by first establishing a new sum-of-squares polynomial representation of convex polynomials over convex semi-algebraic sets under a saddle-point condition. We finally prove that the existence of a saddle-point of the Lagrangian for a convex polynomial program is also necessary for the hierarchy to have finite convergence.Comment: 17 page

Lagrange multiplier characterizations of robust best approximations under constraint data uncertainty

AbstractIn this paper we explain how to characterize the best approximation to any x in a Hilbert space X from the set C∩{x∈X:gi(x)≤0,i=1,2,…,m} in the face of data uncertainty in the convex constraints, gi(x)≤0,i=1,2,…,m, where C is a closed convex subset of X. Following the robust optimization approach, we establish Lagrange multiplier characterizations of the robust constrained best approximation that is immunized against data uncertainty. This is done by characterizing the best approximation to any x from the robust counterpart of the constraints where the constraints are satisfied for all possible uncertainties within the prescribed uncertainty sets. Unlike the traditional Lagrange multiplier characterizations without data uncertainty, for constrained best approximation problems in the face uncertainty, we show that the strong conical hull intersection property (strong CHIP) alone is not sufficient to guarantee the Lagrange multiplier characterizations. We present conditions which guarantee that the strong CHIP is necessary and sufficient for the multiplier characterization. We also establish that the strong CHIP is automatically satisfied for the cases of polyhedral constraints with polytope uncertainty, and linear constraints with interval uncertainty. As an application, we show how robust solutions of shape preserving interpolation problems under ellipsoidal and box uncertainty cases can be obtained in terms of Lagrange multipliers under strict robust feasibility conditions

Effect of Neat Sardine Oil with Varies Blends on the Performance and Emission Characteristics of Diesel Engine

This study investigates the performance and emission characteristics of a diesel engine which is fuelled with neat sardine oil and diesel. A single cylinder four stroke diesel engine was used for the experiments at various load and speed of 1500 rpm. An AVL5 gas analyzer and a smoke meter were used for the measurements of exhaust gas emission. The results showed that break thermal efficiency is decreased and CO (Carbon-monoxide), HC (Hydro-Carbon) in the exhaust is increased when fuelled with neat sardine oil compared to diesel except NOx (Nitrogen Oxide). The future scope of the work is to do some modification (e.g may be engine, piston or values) in the engine to get better performance in same blending ratio

Yield and quality improvement in Bt cotton through foliar application of trifloxystrobin and tebuconazole

In agriculture, fungi can cause serious damage, resulting in critical losses of yield, quality and profit. Fungicides help in reducing the damage caused by fungus, reduce the yield loss and play a major role in quality improvement. The present investigation was carried out at Tamil Nadu Agricultural University to evaluate the influence of trifloxystrobin 50% + tebuconazole 25% (Nativo 75WG) on the yield and quality improvement on Bunny hybrid Bt cotton.  Nativo 75WG was applied on the leaves of cotton plants at 40-60 (DAS) and 60-80 (DAS) at the concentration of 250, 300, 350 g/ha and Carbendazim @ 500 g/ha.  The observations recorded were related to yield and quality attributes in all treatments. The application of Nativo @ 300 g/ha showed a significant increase in boll weight (4.86 g), lint yield per boll (3.86 g boll-1) and lint per plant (138.48 g plant -1) than other treatments. With respect to seed cotton yield and harvest index (0.37 %), the Nativo @ 300 g/ha registered a higher yield (20.2 %) and HI than control under the irrigated situation. Foliar application of treatments during the flowering stage (40-60 DAS) and boll formation stages (60-80 DAS) had increased the quality parameters such as fiber length (2.5% staple length, 50 % staple length) and fiber strength. Further, the foliar spray of  Nativo @ 300 g/ha applied to bunny hybrid Bt cotton had resulted in a higher yield (2920.15 kg ha-1) due to an increase in leaf area index, greenness of leaf and higher dry matter production of the plant

Influence of nutrients and plant growth regulators on growth parameters and yield of Pigeonpea (Cajanus cajan (L.) Millsp.)

Pigeonpea is the second most important pulse crop after chickpea in India. The yield of pigeonpea is very low due to indeterminate growth habit and poor source-sink relationship. Plant growth regulators are known to influence the source-sink relationship and stimulate the translocation of photo-assimilates thereby helping in effective flower formation, fruit and seed development and ultimately enhance productivity of the crops. With this background, a field experiment was conducted with pigeonpea (CO Rg 7) under irrigated condition in Tamil Nadu Agricultural University, Coimbatore. An experiment was aimed at determining the effect of various nutrients and growth-promoting hormones on the growth parameters and yield of pigeonpea (Cajanus cajan (L.) Millsp.). The Factorial Randomised Block Design was used in the field trial and was replicated three times. At the vegetative stage, the treatments included foliar sprays of growth inhibitors such as M2-Mepiquat chloride (MC) @ 500 pp, M3-Chlormequat chloride (CC) @ 500 ppm and M1- Control. At flower initiation and 15 days later, various plant growth regulators, such as T2-SA (100 ppm), T3-BR (0.1 ppm), T4-Napthyl acetic acid (40 ppm), T5-Nutrients (ZnSO4 @ 0.5 percent + H3BO3 @ 0.3 percent, T6-Mono Ammonium Phosphate @ 2 percent, and T7-TNAU Pulse Wonder @ 1 percent), T8-Nutrient consortia I (1%) and T9-Nutrient consortia II (1%), were used. Among the treatments, the combination of Chlormequat chloride and nutrient consortia treatments (M3T8&M3T9) had better performances in growth parameters and yield of pigeonpea (CO Rg 7). Foliar application of M3T8-Chlormequat chloride and Nutrient consortia I (1%) resulted significantly (P<0.05) in the highest Total dry matter production (64.85; 82.96 g plant-1), Leaf area (1629; 1873 cm-2 plant-1), Leaf area index (1.358; 1.561), Specific leaf weight (7.29; 10.34 mg cm-2) and Seed yield (1133 kg ha-1) when compared to other treatments. The present study that the application of a combined formulation of hormones and nutrients present in the nutrient consortia at the flowering and pod formation stages influenced the growth parameters and resulted in higher seed yield